How to find the length of the diagonal of a square - ACT Math

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Question

Find the length of a diagonal of a square whose side length is .

Answer

To solve, simply remember that the diagonal forms an isoceles right triangle. Thus, the diagonal is:

$x\sqrt2=1*\sqrt2=\sqrt2$

Compare your answer with the correct one above

Question

The perimeter of a square is 48. What is the length of its diagonal?

Answer

Perimeter = side * 4

48 = side * 4

Side = 12

We can break up the square into two equal right triangles. The diagonal of the sqaure is then the hypotenuse of these two triangles.

Therefore, we can use the Pythagorean Theorem to solve for the diagonal:

$\sqrt{144+144}=\sqrt{hypotenuse^2}$

$hypotenuse=\sqrt{2\times 144}=\sqrt{2\times 12\times 12}=12\sqrt{2}$

Compare your answer with the correct one above

Question

The perimeter of a square is units. How many units long is the diagonal of the square?

Answer

From the perimeter, we can find the length of each side of the square. The side lengths of a square are equal by definition therefore, the perimeter can be rewritten as,

Then we use the Pythagorean Theorme to find the diagonal, which is the hypotenuse of a right triangle with each leg being a side of the square.

$c=\sqrt{49+49}=\sqrt{98}=\sqrt{2\cdot49}=7\sqrt2$

Compare your answer with the correct one above

Question

What is the area of a square with a diagonal of length ? Round to the nearest hundredth.

Answer

Based on the data provided, the square could be drawn like this:

Based on this, you can use the Pythagorean theorem to find :

or

From this, you know that

Since the area is equal to , this is your answer!

Compare your answer with the correct one above

Question

Find the diagonal of a square with side length .

Answer

To solve, simply realize the triangle that is made by sides and the diagonal is an isoceles right triangle. Thus, the hypotenuse is side length time square root of . Thus,

$s\sqrt2=3\sqrt2$

Compare your answer with the correct one above

Question

Find the length of a diagonal of a square whose side length is .

Answer

To solve, simply remember that the diagonal forms an isoceles right triangle. Thus, the diagonal is:

$x\sqrt2=1*\sqrt2=\sqrt2$

Compare your answer with the correct one above

Question

The perimeter of a square is 48. What is the length of its diagonal?

Answer

Perimeter = side * 4

48 = side * 4

Side = 12

We can break up the square into two equal right triangles. The diagonal of the sqaure is then the hypotenuse of these two triangles.

Therefore, we can use the Pythagorean Theorem to solve for the diagonal:

$\sqrt{144+144}=\sqrt{hypotenuse^2}$

$hypotenuse=\sqrt{2\times 144}=\sqrt{2\times 12\times 12}=12\sqrt{2}$

Compare your answer with the correct one above

Question

The perimeter of a square is units. How many units long is the diagonal of the square?

Answer

From the perimeter, we can find the length of each side of the square. The side lengths of a square are equal by definition therefore, the perimeter can be rewritten as,

Then we use the Pythagorean Theorme to find the diagonal, which is the hypotenuse of a right triangle with each leg being a side of the square.

$c=\sqrt{49+49}=\sqrt{98}=\sqrt{2\cdot49}=7\sqrt2$

Compare your answer with the correct one above

Question

What is the area of a square with a diagonal of length ? Round to the nearest hundredth.

Answer

Based on the data provided, the square could be drawn like this:

Based on this, you can use the Pythagorean theorem to find :

or

From this, you know that

Since the area is equal to , this is your answer!

Compare your answer with the correct one above

Question

Find the diagonal of a square with side length .

Answer

To solve, simply realize the triangle that is made by sides and the diagonal is an isoceles right triangle. Thus, the hypotenuse is side length time square root of . Thus,

$s\sqrt2=3\sqrt2$

Compare your answer with the correct one above

Question

Find the length of a diagonal of a square whose side length is .

Answer

To solve, simply remember that the diagonal forms an isoceles right triangle. Thus, the diagonal is:

$x\sqrt2=1*\sqrt2=\sqrt2$

Compare your answer with the correct one above

Question

The perimeter of a square is 48. What is the length of its diagonal?

Answer

Perimeter = side * 4

48 = side * 4

Side = 12

We can break up the square into two equal right triangles. The diagonal of the sqaure is then the hypotenuse of these two triangles.

Therefore, we can use the Pythagorean Theorem to solve for the diagonal:

$\sqrt{144+144}=\sqrt{hypotenuse^2}$

$hypotenuse=\sqrt{2\times 144}=\sqrt{2\times 12\times 12}=12\sqrt{2}$

Compare your answer with the correct one above

Question

The perimeter of a square is units. How many units long is the diagonal of the square?

Answer

From the perimeter, we can find the length of each side of the square. The side lengths of a square are equal by definition therefore, the perimeter can be rewritten as,

Then we use the Pythagorean Theorme to find the diagonal, which is the hypotenuse of a right triangle with each leg being a side of the square.

$c=\sqrt{49+49}=\sqrt{98}=\sqrt{2\cdot49}=7\sqrt2$

Compare your answer with the correct one above

Question

What is the area of a square with a diagonal of length ? Round to the nearest hundredth.

Answer

Based on the data provided, the square could be drawn like this:

Based on this, you can use the Pythagorean theorem to find :

or

From this, you know that

Since the area is equal to , this is your answer!

Compare your answer with the correct one above

Question

Find the diagonal of a square with side length .

Answer

To solve, simply realize the triangle that is made by sides and the diagonal is an isoceles right triangle. Thus, the hypotenuse is side length time square root of . Thus,

$s\sqrt2=3\sqrt2$

Compare your answer with the correct one above

Question

Find the length of a diagonal of a square whose side length is .

Answer

To solve, simply remember that the diagonal forms an isoceles right triangle. Thus, the diagonal is:

$x\sqrt2=1*\sqrt2=\sqrt2$

Compare your answer with the correct one above

Question

The perimeter of a square is 48. What is the length of its diagonal?

Answer

Perimeter = side * 4

48 = side * 4

Side = 12

We can break up the square into two equal right triangles. The diagonal of the sqaure is then the hypotenuse of these two triangles.

Therefore, we can use the Pythagorean Theorem to solve for the diagonal:

$\sqrt{144+144}=\sqrt{hypotenuse^2}$

$hypotenuse=\sqrt{2\times 144}=\sqrt{2\times 12\times 12}=12\sqrt{2}$

Compare your answer with the correct one above

Question

The perimeter of a square is units. How many units long is the diagonal of the square?

Answer

From the perimeter, we can find the length of each side of the square. The side lengths of a square are equal by definition therefore, the perimeter can be rewritten as,

Then we use the Pythagorean Theorme to find the diagonal, which is the hypotenuse of a right triangle with each leg being a side of the square.

$c=\sqrt{49+49}=\sqrt{98}=\sqrt{2\cdot49}=7\sqrt2$

Compare your answer with the correct one above

Question

What is the area of a square with a diagonal of length ? Round to the nearest hundredth.

Answer

Based on the data provided, the square could be drawn like this:

Based on this, you can use the Pythagorean theorem to find :

or

From this, you know that

Since the area is equal to , this is your answer!

Compare your answer with the correct one above

Question

Find the diagonal of a square with side length .

Answer

To solve, simply realize the triangle that is made by sides and the diagonal is an isoceles right triangle. Thus, the hypotenuse is side length time square root of . Thus,

$s\sqrt2=3\sqrt2$

Compare your answer with the correct one above

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How to find the length of the diagonal of a square - ACT Math

Find the length of a diagonal of a square whose side length is .

To solve, simply remember that the diagonal forms an isoceles right triangle. Thus, the diagonal is:

The perimeter of a square is 48. What is the length of its diagonal?

Perimeter = side * 4 48 = side * 4 Side = 12 We can break up the square into two equal right triangles. The diagonal of the sqaure is then the hypotenuse of these two triangles. Therefore, we can use the Pythagorean Theorem to solve for the diagonal:

The perimeter of a square is units. How many units long is the diagonal of the square?

What is the area of a square with a diagonal of length ? Round to the nearest hundredth.

Based on the data provided, the square could be drawn like this: Based on this, you can use the Pythagorean theorem to find : or From this, you know that Since the area is equal to , this is your answer!

Find the diagonal of a square with side length .

To solve, simply realize the triangle that is made by sides and the diagonal is an isoceles right triangle. Thus, the hypotenuse is side length time square root of . Thus,

Find the length of a diagonal of a square whose side length is .

To solve, simply remember that the diagonal forms an isoceles right triangle. Thus, the diagonal is:

The perimeter of a square is 48. What is the length of its diagonal?

Perimeter = side * 4 48 = side * 4 Side = 12 We can break up the square into two equal right triangles. The diagonal of the sqaure is then the hypotenuse of these two triangles. Therefore, we can use the Pythagorean Theorem to solve for the diagonal:

The perimeter of a square is units. How many units long is the diagonal of the square?

What is the area of a square with a diagonal of length ? Round to the nearest hundredth.

Based on the data provided, the square could be drawn like this: Based on this, you can use the Pythagorean theorem to find : or From this, you know that Since the area is equal to , this is your answer!

Find the diagonal of a square with side length .

To solve, simply realize the triangle that is made by sides and the diagonal is an isoceles right triangle. Thus, the hypotenuse is side length time square root of . Thus,

Find the length of a diagonal of a square whose side length is .

To solve, simply remember that the diagonal forms an isoceles right triangle. Thus, the diagonal is:

The perimeter of a square is 48. What is the length of its diagonal?

Perimeter = side * 4 48 = side * 4 Side = 12 We can break up the square into two equal right triangles. The diagonal of the sqaure is then the hypotenuse of these two triangles. Therefore, we can use the Pythagorean Theorem to solve for the diagonal:

The perimeter of a square is units. How many units long is the diagonal of the square?

What is the area of a square with a diagonal of length ? Round to the nearest hundredth.

Based on the data provided, the square could be drawn like this: Based on this, you can use the Pythagorean theorem to find : or From this, you know that Since the area is equal to , this is your answer!

Find the diagonal of a square with side length .

To solve, simply realize the triangle that is made by sides and the diagonal is an isoceles right triangle. Thus, the hypotenuse is side length time square root of . Thus,

Find the length of a diagonal of a square whose side length is .

To solve, simply remember that the diagonal forms an isoceles right triangle. Thus, the diagonal is:

The perimeter of a square is 48. What is the length of its diagonal?

Perimeter = side * 4 48 = side * 4 Side = 12 We can break up the square into two equal right triangles. The diagonal of the sqaure is then the hypotenuse of these two triangles. Therefore, we can use the Pythagorean Theorem to solve for the diagonal:

The perimeter of a square is units. How many units long is the diagonal of the square?

What is the area of a square with a diagonal of length ? Round to the nearest hundredth.

Based on the data provided, the square could be drawn like this: Based on this, you can use the Pythagorean theorem to find : or From this, you know that Since the area is equal to , this is your answer!

Find the diagonal of a square with side length .

To solve, simply realize the triangle that is made by sides and the diagonal is an isoceles right triangle. Thus, the hypotenuse is side length time square root of . Thus,

To solve, simply remember that the diagonal forms an isoceles right triangle. Thus, the diagonal is:

$x\sqrt2=1*\sqrt2=\sqrt2$

Based on the data provided, the square could be drawn like this:

Based on this, you can use the Pythagorean theorem to find :

or

From this, you know that

Since the area is equal to , this is your answer!

To solve, simply realize the triangle that is made by sides and the diagonal is an isoceles right triangle. Thus, the hypotenuse is side length time square root of . Thus,

$s\sqrt2=3\sqrt2$

To solve, simply remember that the diagonal forms an isoceles right triangle. Thus, the diagonal is:

$x\sqrt2=1*\sqrt2=\sqrt2$

Based on the data provided, the square could be drawn like this:

Based on this, you can use the Pythagorean theorem to find :

or

From this, you know that

Since the area is equal to , this is your answer!

To solve, simply realize the triangle that is made by sides and the diagonal is an isoceles right triangle. Thus, the hypotenuse is side length time square root of . Thus,

$s\sqrt2=3\sqrt2$

To solve, simply remember that the diagonal forms an isoceles right triangle. Thus, the diagonal is:

$x\sqrt2=1*\sqrt2=\sqrt2$

Based on the data provided, the square could be drawn like this:

Based on this, you can use the Pythagorean theorem to find :

or

From this, you know that

Since the area is equal to , this is your answer!

To solve, simply realize the triangle that is made by sides and the diagonal is an isoceles right triangle. Thus, the hypotenuse is side length time square root of . Thus,

$s\sqrt2=3\sqrt2$

To solve, simply remember that the diagonal forms an isoceles right triangle. Thus, the diagonal is:

$x\sqrt2=1*\sqrt2=\sqrt2$

Based on the data provided, the square could be drawn like this:

Based on this, you can use the Pythagorean theorem to find :

or

From this, you know that

Since the area is equal to , this is your answer!

To solve, simply realize the triangle that is made by sides and the diagonal is an isoceles right triangle. Thus, the hypotenuse is side length time square root of . Thus,

$s\sqrt2=3\sqrt2$