How to find the length of the side of an equilateral triangle - GRE Quantitative Reasoning

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Question

What is the length of a side of an equilateral triangle if the area is $9\sqrt{3}$ ?

Answer

The area of an equilateral triangle is $\frac{s^2\sqrt{3}}{4}$ .

So let's set-up an equation to solve for .

$\frac{s^2\sqrt{3}}{4}=9\sqrt{3}$ Cross multiply.

$s^2\sqrt{3}=36\sqrt{3}$

The $\sqrt{3}$ cancels out and we get .

Then take square root on both sides and we get as the final answer.

Compare your answer with the correct one above

Question

If the height of the equilateral triangle is $4\sqrt{2}$ , then what is the length of a side of an equilateral triangle?

Answer

By having a height in an equilateral triangle, the angle is bisected therefore creating two triangles.

The height is opposite the angle . We can set-up a proportion.

Side opposite is $\sqrt{3}$ and the side of equilateral triangle which is opposite is .

$\frac{4\sqrt{2}}{\sqrt{3}}=\frac{s}{2}$ Cross multiply.

$8\sqrt{2}=s\sqrt{3}$ Divide both sides by $\sqrt{3}$

$\frac{8\sqrt{2}}{\sqrt{3}}=s$ Multiply top and bottom by $\sqrt{3}$ to get rid of the radical.

$\frac{8\sqrt{6}}{3}=s$

Compare your answer with the correct one above

Question

What is the length of a side of an equilateral triangle if the area is $9\sqrt{3}$ ?

Answer

The area of an equilateral triangle is $\frac{s^2\sqrt{3}}{4}$ .

So let's set-up an equation to solve for .

$\frac{s^2\sqrt{3}}{4}=9\sqrt{3}$ Cross multiply.

$s^2\sqrt{3}=36\sqrt{3}$

The $\sqrt{3}$ cancels out and we get .

Then take square root on both sides and we get as the final answer.

Compare your answer with the correct one above

Question

If the height of the equilateral triangle is $4\sqrt{2}$ , then what is the length of a side of an equilateral triangle?

Answer

By having a height in an equilateral triangle, the angle is bisected therefore creating two triangles.

The height is opposite the angle . We can set-up a proportion.

Side opposite is $\sqrt{3}$ and the side of equilateral triangle which is opposite is .

$\frac{4\sqrt{2}}{\sqrt{3}}=\frac{s}{2}$ Cross multiply.

$8\sqrt{2}=s\sqrt{3}$ Divide both sides by $\sqrt{3}$

$\frac{8\sqrt{2}}{\sqrt{3}}=s$ Multiply top and bottom by $\sqrt{3}$ to get rid of the radical.

$\frac{8\sqrt{6}}{3}=s$

Compare your answer with the correct one above

Question

What is the length of a side of an equilateral triangle if the area is $9\sqrt{3}$ ?

Answer

The area of an equilateral triangle is $\frac{s^2\sqrt{3}}{4}$ .

So let's set-up an equation to solve for .

$\frac{s^2\sqrt{3}}{4}=9\sqrt{3}$ Cross multiply.

$s^2\sqrt{3}=36\sqrt{3}$

The $\sqrt{3}$ cancels out and we get .

Then take square root on both sides and we get as the final answer.

Compare your answer with the correct one above

Question

If the height of the equilateral triangle is $4\sqrt{2}$ , then what is the length of a side of an equilateral triangle?

Answer

By having a height in an equilateral triangle, the angle is bisected therefore creating two triangles.

The height is opposite the angle . We can set-up a proportion.

Side opposite is $\sqrt{3}$ and the side of equilateral triangle which is opposite is .

$\frac{4\sqrt{2}}{\sqrt{3}}=\frac{s}{2}$ Cross multiply.

$8\sqrt{2}=s\sqrt{3}$ Divide both sides by $\sqrt{3}$

$\frac{8\sqrt{2}}{\sqrt{3}}=s$ Multiply top and bottom by $\sqrt{3}$ to get rid of the radical.

$\frac{8\sqrt{6}}{3}=s$

Compare your answer with the correct one above

Question

What is the length of a side of an equilateral triangle if the area is $9\sqrt{3}$ ?

Answer

The area of an equilateral triangle is $\frac{s^2\sqrt{3}}{4}$ .

So let's set-up an equation to solve for .

$\frac{s^2\sqrt{3}}{4}=9\sqrt{3}$ Cross multiply.

$s^2\sqrt{3}=36\sqrt{3}$

The $\sqrt{3}$ cancels out and we get .

Then take square root on both sides and we get as the final answer.

Compare your answer with the correct one above

Question

If the height of the equilateral triangle is $4\sqrt{2}$ , then what is the length of a side of an equilateral triangle?

Answer

By having a height in an equilateral triangle, the angle is bisected therefore creating two triangles.

The height is opposite the angle . We can set-up a proportion.

Side opposite is $\sqrt{3}$ and the side of equilateral triangle which is opposite is .

$\frac{4\sqrt{2}}{\sqrt{3}}=\frac{s}{2}$ Cross multiply.

$8\sqrt{2}=s\sqrt{3}$ Divide both sides by $\sqrt{3}$

$\frac{8\sqrt{2}}{\sqrt{3}}=s$ Multiply top and bottom by $\sqrt{3}$ to get rid of the radical.

$\frac{8\sqrt{6}}{3}=s$

Compare your answer with the correct one above

Question

What is the length of a side of an equilateral triangle if the area is $9\sqrt{3}$ ?

Answer

The area of an equilateral triangle is $\frac{s^2\sqrt{3}}{4}$ .

So let's set-up an equation to solve for .

$\frac{s^2\sqrt{3}}{4}=9\sqrt{3}$ Cross multiply.

$s^2\sqrt{3}=36\sqrt{3}$

The $\sqrt{3}$ cancels out and we get .

Then take square root on both sides and we get as the final answer.

Compare your answer with the correct one above

Question

If the height of the equilateral triangle is $4\sqrt{2}$ , then what is the length of a side of an equilateral triangle?

Answer

By having a height in an equilateral triangle, the angle is bisected therefore creating two triangles.

The height is opposite the angle . We can set-up a proportion.

Side opposite is $\sqrt{3}$ and the side of equilateral triangle which is opposite is .

$\frac{4\sqrt{2}}{\sqrt{3}}=\frac{s}{2}$ Cross multiply.

$8\sqrt{2}=s\sqrt{3}$ Divide both sides by $\sqrt{3}$

$\frac{8\sqrt{2}}{\sqrt{3}}=s$ Multiply top and bottom by $\sqrt{3}$ to get rid of the radical.

$\frac{8\sqrt{6}}{3}=s$

Compare your answer with the correct one above

Question

What is the length of a side of an equilateral triangle if the area is $9\sqrt{3}$ ?

Answer

The area of an equilateral triangle is $\frac{s^2\sqrt{3}}{4}$ .

So let's set-up an equation to solve for .

$\frac{s^2\sqrt{3}}{4}=9\sqrt{3}$ Cross multiply.

$s^2\sqrt{3}=36\sqrt{3}$

The $\sqrt{3}$ cancels out and we get .

Then take square root on both sides and we get as the final answer.

Compare your answer with the correct one above

Question

If the height of the equilateral triangle is $4\sqrt{2}$ , then what is the length of a side of an equilateral triangle?

Answer

By having a height in an equilateral triangle, the angle is bisected therefore creating two triangles.

The height is opposite the angle . We can set-up a proportion.

Side opposite is $\sqrt{3}$ and the side of equilateral triangle which is opposite is .

$\frac{4\sqrt{2}}{\sqrt{3}}=\frac{s}{2}$ Cross multiply.

$8\sqrt{2}=s\sqrt{3}$ Divide both sides by $\sqrt{3}$

$\frac{8\sqrt{2}}{\sqrt{3}}=s$ Multiply top and bottom by $\sqrt{3}$ to get rid of the radical.

$\frac{8\sqrt{6}}{3}=s$

Compare your answer with the correct one above

Question

What is the length of a side of an equilateral triangle if the area is $9\sqrt{3}$ ?

Answer

The area of an equilateral triangle is $\frac{s^2\sqrt{3}}{4}$ .

So let's set-up an equation to solve for .

$\frac{s^2\sqrt{3}}{4}=9\sqrt{3}$ Cross multiply.

$s^2\sqrt{3}=36\sqrt{3}$

The $\sqrt{3}$ cancels out and we get .

Then take square root on both sides and we get as the final answer.

Compare your answer with the correct one above

Question

If the height of the equilateral triangle is $4\sqrt{2}$ , then what is the length of a side of an equilateral triangle?

Answer

By having a height in an equilateral triangle, the angle is bisected therefore creating two triangles.

The height is opposite the angle . We can set-up a proportion.

Side opposite is $\sqrt{3}$ and the side of equilateral triangle which is opposite is .

$\frac{4\sqrt{2}}{\sqrt{3}}=\frac{s}{2}$ Cross multiply.

$8\sqrt{2}=s\sqrt{3}$ Divide both sides by $\sqrt{3}$

$\frac{8\sqrt{2}}{\sqrt{3}}=s$ Multiply top and bottom by $\sqrt{3}$ to get rid of the radical.

$\frac{8\sqrt{6}}{3}=s$

Compare your answer with the correct one above

Question

What is the length of a side of an equilateral triangle if the area is $9\sqrt{3}$ ?

Answer

The area of an equilateral triangle is $\frac{s^2\sqrt{3}}{4}$ .

So let's set-up an equation to solve for .

$\frac{s^2\sqrt{3}}{4}=9\sqrt{3}$ Cross multiply.

$s^2\sqrt{3}=36\sqrt{3}$

The $\sqrt{3}$ cancels out and we get .

Then take square root on both sides and we get as the final answer.

Compare your answer with the correct one above

Question

If the height of the equilateral triangle is $4\sqrt{2}$ , then what is the length of a side of an equilateral triangle?

Answer

By having a height in an equilateral triangle, the angle is bisected therefore creating two triangles.

The height is opposite the angle . We can set-up a proportion.

Side opposite is $\sqrt{3}$ and the side of equilateral triangle which is opposite is .

$\frac{4\sqrt{2}}{\sqrt{3}}=\frac{s}{2}$ Cross multiply.

$8\sqrt{2}=s\sqrt{3}$ Divide both sides by $\sqrt{3}$

$\frac{8\sqrt{2}}{\sqrt{3}}=s$ Multiply top and bottom by $\sqrt{3}$ to get rid of the radical.

$\frac{8\sqrt{6}}{3}=s$

Compare your answer with the correct one above

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How to find the length of the side of an equilateral triangle - GRE Quantitative Reasoning

What is the length of a side of an equilateral triangle if the area is ?

The area of an equilateral triangle is . So let's set-up an equation to solve for . Cross multiply. The cancels out and we get . Then take square root on both sides and we get as the final answer.

If the height of the equilateral triangle is , then what is the length of a side of an equilateral triangle?

What is the length of a side of an equilateral triangle if the area is ?

The area of an equilateral triangle is . So let's set-up an equation to solve for . Cross multiply. The cancels out and we get . Then take square root on both sides and we get as the final answer.

If the height of the equilateral triangle is , then what is the length of a side of an equilateral triangle?

What is the length of a side of an equilateral triangle if the area is ?

The area of an equilateral triangle is . So let's set-up an equation to solve for . Cross multiply. The cancels out and we get . Then take square root on both sides and we get as the final answer.

If the height of the equilateral triangle is , then what is the length of a side of an equilateral triangle?

What is the length of a side of an equilateral triangle if the area is ?

The area of an equilateral triangle is . So let's set-up an equation to solve for . Cross multiply. The cancels out and we get . Then take square root on both sides and we get as the final answer.

If the height of the equilateral triangle is , then what is the length of a side of an equilateral triangle?

What is the length of a side of an equilateral triangle if the area is ?

The area of an equilateral triangle is . So let's set-up an equation to solve for . Cross multiply. The cancels out and we get . Then take square root on both sides and we get as the final answer.

If the height of the equilateral triangle is , then what is the length of a side of an equilateral triangle?

What is the length of a side of an equilateral triangle if the area is ?

The area of an equilateral triangle is . So let's set-up an equation to solve for . Cross multiply. The cancels out and we get . Then take square root on both sides and we get as the final answer.

If the height of the equilateral triangle is , then what is the length of a side of an equilateral triangle?

What is the length of a side of an equilateral triangle if the area is ?

The area of an equilateral triangle is . So let's set-up an equation to solve for . Cross multiply. The cancels out and we get . Then take square root on both sides and we get as the final answer.

If the height of the equilateral triangle is , then what is the length of a side of an equilateral triangle?

What is the length of a side of an equilateral triangle if the area is ?

The area of an equilateral triangle is . So let's set-up an equation to solve for . Cross multiply. The cancels out and we get . Then take square root on both sides and we get as the final answer.

If the height of the equilateral triangle is , then what is the length of a side of an equilateral triangle?

What is the length of a side of an equilateral triangle if the area is $9\sqrt{3}$ ?

The area of an equilateral triangle is $\frac{s^2\sqrt{3}}{4}$ .

So let's set-up an equation to solve for .

$\frac{s^2\sqrt{3}}{4}=9\sqrt{3}$ Cross multiply.

$s^2\sqrt{3}=36\sqrt{3}$

The $\sqrt{3}$ cancels out and we get .

Then take square root on both sides and we get as the final answer.

If the height of the equilateral triangle is $4\sqrt{2}$ , then what is the length of a side of an equilateral triangle?

What is the length of a side of an equilateral triangle if the area is $9\sqrt{3}$ ?

The area of an equilateral triangle is $\frac{s^2\sqrt{3}}{4}$ .

So let's set-up an equation to solve for .

$\frac{s^2\sqrt{3}}{4}=9\sqrt{3}$ Cross multiply.

$s^2\sqrt{3}=36\sqrt{3}$

The $\sqrt{3}$ cancels out and we get .

Then take square root on both sides and we get as the final answer.

If the height of the equilateral triangle is $4\sqrt{2}$ , then what is the length of a side of an equilateral triangle?

What is the length of a side of an equilateral triangle if the area is $9\sqrt{3}$ ?

The area of an equilateral triangle is $\frac{s^2\sqrt{3}}{4}$ .

So let's set-up an equation to solve for .

$\frac{s^2\sqrt{3}}{4}=9\sqrt{3}$ Cross multiply.

$s^2\sqrt{3}=36\sqrt{3}$

The $\sqrt{3}$ cancels out and we get .

Then take square root on both sides and we get as the final answer.

If the height of the equilateral triangle is $4\sqrt{2}$ , then what is the length of a side of an equilateral triangle?

What is the length of a side of an equilateral triangle if the area is $9\sqrt{3}$ ?

The area of an equilateral triangle is $\frac{s^2\sqrt{3}}{4}$ .

So let's set-up an equation to solve for .

$\frac{s^2\sqrt{3}}{4}=9\sqrt{3}$ Cross multiply.

$s^2\sqrt{3}=36\sqrt{3}$

The $\sqrt{3}$ cancels out and we get .

Then take square root on both sides and we get as the final answer.

If the height of the equilateral triangle is $4\sqrt{2}$ , then what is the length of a side of an equilateral triangle?

What is the length of a side of an equilateral triangle if the area is $9\sqrt{3}$ ?

The area of an equilateral triangle is $\frac{s^2\sqrt{3}}{4}$ .

So let's set-up an equation to solve for .

$\frac{s^2\sqrt{3}}{4}=9\sqrt{3}$ Cross multiply.

$s^2\sqrt{3}=36\sqrt{3}$

The $\sqrt{3}$ cancels out and we get .

Then take square root on both sides and we get as the final answer.

If the height of the equilateral triangle is $4\sqrt{2}$ , then what is the length of a side of an equilateral triangle?

What is the length of a side of an equilateral triangle if the area is $9\sqrt{3}$ ?

The area of an equilateral triangle is $\frac{s^2\sqrt{3}}{4}$ .

So let's set-up an equation to solve for .

$\frac{s^2\sqrt{3}}{4}=9\sqrt{3}$ Cross multiply.

$s^2\sqrt{3}=36\sqrt{3}$

The $\sqrt{3}$ cancels out and we get .

Then take square root on both sides and we get as the final answer.

If the height of the equilateral triangle is $4\sqrt{2}$ , then what is the length of a side of an equilateral triangle?

What is the length of a side of an equilateral triangle if the area is $9\sqrt{3}$ ?

The area of an equilateral triangle is $\frac{s^2\sqrt{3}}{4}$ .

So let's set-up an equation to solve for .

$\frac{s^2\sqrt{3}}{4}=9\sqrt{3}$ Cross multiply.

$s^2\sqrt{3}=36\sqrt{3}$

The $\sqrt{3}$ cancels out and we get .

Then take square root on both sides and we get as the final answer.

If the height of the equilateral triangle is $4\sqrt{2}$ , then what is the length of a side of an equilateral triangle?

What is the length of a side of an equilateral triangle if the area is $9\sqrt{3}$ ?

The area of an equilateral triangle is $\frac{s^2\sqrt{3}}{4}$ .

So let's set-up an equation to solve for .

$\frac{s^2\sqrt{3}}{4}=9\sqrt{3}$ Cross multiply.

$s^2\sqrt{3}=36\sqrt{3}$

The $\sqrt{3}$ cancels out and we get .

Then take square root on both sides and we get as the final answer.

If the height of the equilateral triangle is $4\sqrt{2}$ , then what is the length of a side of an equilateral triangle?