How to find the perimeter of an equilateral triangle - ACT Math

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Question

What is the perimeter of an equilateral triangle with an area of $56.25\sqrt{3}$ ?

Answer

Recall that from any vertex of an equilateral triangle, you can drop a height that is a bisector of that vertex as well as a bisector of the correlative side. This gives you the following figure:

Notice that the small triangles within the larger triangle are both triangles. Therefore, you can create a ratio to help you find .

The ratio of the small base to the height is the same as $1:\sqrt{3}$ . Therefore, you can write the following equation:

$\frac{0.5b}{h}=\frac{1}{\sqrt{3}}$

This means that $0.5b\sqrt{3}=h$ .

Now, the area of a triangle can be written:

$A=\frac{1}{2}bh$ , and based on our data, we can replace with $\frac{b\sqrt{3}}{2}$ . This gives you:

$56.25\sqrt{3}=\frac{1}{2}b\frac{b\sqrt{3}}{2}=\frac{b^2\sqrt{3}}{4}$

Now, let's write that a bit more simply:

$56.25\sqrt{3}=\frac{b^2\sqrt{3}}{4}$

Solve for . Begin by multiplying each side by :

$225\sqrt{3}=b^2\sqrt{3}$

Divide each side by $\sqrt3$ :

Finally, take the square root of both sides. This gives you . Therefore, the perimeter is .

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Question

An equilateral triangle with a perimeter of has sides with what length?

Answer

An equilateral triangle has 3 equal length sides.

Therefore the perimeter equation is as follows,

.

So divide the perimeter by 3 to find the length of each side.

Thus the answer is:

$\frac{48}{3}=s$

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Question

Jill has an equilateral triangular garden with a base of and one leg with a length of , what is the perimeter?

Answer

Since the triangle is equilateral, the base and the legs are equal, so the first step is to set the two equations equal to each other. Start with , add to both sides giving you . Subtract from both sides, leaving . Finally divide both sides by , so you're left with . Plug back in for into either of the equations so that you get a side length of . To find the perimeter, multiply the side length $\left ( 34\right )$ , by , giving you .

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Question

Find the perimeter of an equilateral triangle whose side length is

Answer

To find perimeter of an quilateral triangle, simply multiply the side length by . Thus,

$P=s\cdot3=2.1\cdot3=6.3$

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Question

Find the perimeter of an equilateral triangle whose side length is .

Answer

To solve, simply multiply the side length by . Thus,

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Question

Find the perimeter of an equilateral triangle given side length of 2.

Answer

To solve, simply multiply the side length by 3 since they are all equal. Thus,

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Question

What is the perimeter of an equilateral triangle with an area of $56.25\sqrt{3}$ ?

Answer

Recall that from any vertex of an equilateral triangle, you can drop a height that is a bisector of that vertex as well as a bisector of the correlative side. This gives you the following figure:

Notice that the small triangles within the larger triangle are both triangles. Therefore, you can create a ratio to help you find .

The ratio of the small base to the height is the same as $1:\sqrt{3}$ . Therefore, you can write the following equation:

$\frac{0.5b}{h}=\frac{1}{\sqrt{3}}$

This means that $0.5b\sqrt{3}=h$ .

Now, the area of a triangle can be written:

$A=\frac{1}{2}bh$ , and based on our data, we can replace with $\frac{b\sqrt{3}}{2}$ . This gives you:

$56.25\sqrt{3}=\frac{1}{2}b\frac{b\sqrt{3}}{2}=\frac{b^2\sqrt{3}}{4}$

Now, let's write that a bit more simply:

$56.25\sqrt{3}=\frac{b^2\sqrt{3}}{4}$

Solve for . Begin by multiplying each side by :

$225\sqrt{3}=b^2\sqrt{3}$

Divide each side by $\sqrt3$ :

Finally, take the square root of both sides. This gives you . Therefore, the perimeter is .

Compare your answer with the correct one above

Question

An equilateral triangle with a perimeter of has sides with what length?

Answer

An equilateral triangle has 3 equal length sides.

Therefore the perimeter equation is as follows,

.

So divide the perimeter by 3 to find the length of each side.

Thus the answer is:

$\frac{48}{3}=s$

Compare your answer with the correct one above

Question

Jill has an equilateral triangular garden with a base of and one leg with a length of , what is the perimeter?

Answer

Since the triangle is equilateral, the base and the legs are equal, so the first step is to set the two equations equal to each other. Start with , add to both sides giving you . Subtract from both sides, leaving . Finally divide both sides by , so you're left with . Plug back in for into either of the equations so that you get a side length of . To find the perimeter, multiply the side length $\left ( 34\right )$ , by , giving you .

Compare your answer with the correct one above

Question

Find the perimeter of an equilateral triangle whose side length is

Answer

To find perimeter of an quilateral triangle, simply multiply the side length by . Thus,

$P=s\cdot3=2.1\cdot3=6.3$

Compare your answer with the correct one above

Question

Find the perimeter of an equilateral triangle whose side length is .

Answer

To solve, simply multiply the side length by . Thus,

Compare your answer with the correct one above

Question

Find the perimeter of an equilateral triangle given side length of 2.

Answer

To solve, simply multiply the side length by 3 since they are all equal. Thus,

Compare your answer with the correct one above

Question

What is the perimeter of an equilateral triangle with an area of $56.25\sqrt{3}$ ?

Answer

Recall that from any vertex of an equilateral triangle, you can drop a height that is a bisector of that vertex as well as a bisector of the correlative side. This gives you the following figure:

Notice that the small triangles within the larger triangle are both triangles. Therefore, you can create a ratio to help you find .

The ratio of the small base to the height is the same as $1:\sqrt{3}$ . Therefore, you can write the following equation:

$\frac{0.5b}{h}=\frac{1}{\sqrt{3}}$

This means that $0.5b\sqrt{3}=h$ .

Now, the area of a triangle can be written:

$A=\frac{1}{2}bh$ , and based on our data, we can replace with $\frac{b\sqrt{3}}{2}$ . This gives you:

$56.25\sqrt{3}=\frac{1}{2}b\frac{b\sqrt{3}}{2}=\frac{b^2\sqrt{3}}{4}$

Now, let's write that a bit more simply:

$56.25\sqrt{3}=\frac{b^2\sqrt{3}}{4}$

Solve for . Begin by multiplying each side by :

$225\sqrt{3}=b^2\sqrt{3}$

Divide each side by $\sqrt3$ :

Finally, take the square root of both sides. This gives you . Therefore, the perimeter is .

Compare your answer with the correct one above

Question

An equilateral triangle with a perimeter of has sides with what length?

Answer

An equilateral triangle has 3 equal length sides.

Therefore the perimeter equation is as follows,

.

So divide the perimeter by 3 to find the length of each side.

Thus the answer is:

$\frac{48}{3}=s$

Compare your answer with the correct one above

Question

Jill has an equilateral triangular garden with a base of and one leg with a length of , what is the perimeter?

Answer

Since the triangle is equilateral, the base and the legs are equal, so the first step is to set the two equations equal to each other. Start with , add to both sides giving you . Subtract from both sides, leaving . Finally divide both sides by , so you're left with . Plug back in for into either of the equations so that you get a side length of . To find the perimeter, multiply the side length $\left ( 34\right )$ , by , giving you .

Compare your answer with the correct one above

Question

Find the perimeter of an equilateral triangle whose side length is

Answer

To find perimeter of an quilateral triangle, simply multiply the side length by . Thus,

$P=s\cdot3=2.1\cdot3=6.3$

Compare your answer with the correct one above

Question

Find the perimeter of an equilateral triangle whose side length is .

Answer

To solve, simply multiply the side length by . Thus,

Compare your answer with the correct one above

Question

Find the perimeter of an equilateral triangle given side length of 2.

Answer

To solve, simply multiply the side length by 3 since they are all equal. Thus,

Compare your answer with the correct one above

Question

What is the perimeter of an equilateral triangle with an area of $56.25\sqrt{3}$ ?

Answer

Recall that from any vertex of an equilateral triangle, you can drop a height that is a bisector of that vertex as well as a bisector of the correlative side. This gives you the following figure:

Notice that the small triangles within the larger triangle are both triangles. Therefore, you can create a ratio to help you find .

The ratio of the small base to the height is the same as $1:\sqrt{3}$ . Therefore, you can write the following equation:

$\frac{0.5b}{h}=\frac{1}{\sqrt{3}}$

This means that $0.5b\sqrt{3}=h$ .

Now, the area of a triangle can be written:

$A=\frac{1}{2}bh$ , and based on our data, we can replace with $\frac{b\sqrt{3}}{2}$ . This gives you:

$56.25\sqrt{3}=\frac{1}{2}b\frac{b\sqrt{3}}{2}=\frac{b^2\sqrt{3}}{4}$

Now, let's write that a bit more simply:

$56.25\sqrt{3}=\frac{b^2\sqrt{3}}{4}$

Solve for . Begin by multiplying each side by :

$225\sqrt{3}=b^2\sqrt{3}$

Divide each side by $\sqrt3$ :

Finally, take the square root of both sides. This gives you . Therefore, the perimeter is .

Compare your answer with the correct one above

Question

An equilateral triangle with a perimeter of has sides with what length?

Answer

An equilateral triangle has 3 equal length sides.

Therefore the perimeter equation is as follows,

.

So divide the perimeter by 3 to find the length of each side.

Thus the answer is:

$\frac{48}{3}=s$

Compare your answer with the correct one above

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