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Basic Geometry : How to find the length of the diagonal of a square

Study concepts, example questions & explanations for Basic Geometry

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Example Questions

Example Question #11 : Squares

Find the length of the diagonal of a square with side lengths of .

Possible Answers:

$3\sqrt2$

$9\sqrt2$

$6\sqrt2$

Correct answer:

$3\sqrt2$

Explanation:

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of the diagonal.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

$\text{Diagonal}=\sqrt{2(\text{side length})^2}$

$\text{Diagonal}=(\text{side length})\sqrt2$

For the square given in the question,

$\text{Diagonal}=3\sqrt2$

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Example Question #261 : Quadrilaterals

Find the length of the diagonal of a square with side lengths of .

Possible Answers:

$11\sqrt2$

$16\sqrt2$

$22\sqrt2$

$15\sqrt2$

Correct answer:

$22\sqrt2$

Explanation:

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of the diagonal.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

$\text{Diagonal}=\sqrt{2(\text{side length})^2}$

$\text{Diagonal}=(\text{side length})\sqrt2$

For the square given in the question,

$\text{Diagonal}=22\sqrt2$

Report an Error

Example Question #262 : Quadrilaterals

Find the length of the diagonal of a square with a side length of .

Possible Answers:

$6\sqrt2$

$16\sqrt2$

$12\sqrt2$

Correct answer:

$12\sqrt2$

Explanation:

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of the diagonal.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

$\text{Diagonal}=\sqrt{2(\text{side length})^2}$

$\text{Diagonal}=(\text{side length})\sqrt2$

For the square given in the question,

$\text{Diagonal}=12\sqrt2$

Report an Error

Example Question #12 : Squares

Find the length of the diagonal of a square that has a side length of .

Possible Answers:

$5\sqrt2$

2.5

$10\sqrt2$

Correct answer:

$5\sqrt2$

Explanation:

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of the diagonal.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

$\text{Diagonal}=\sqrt{2(\text{side length})^2}$

$\text{Diagonal}=(\text{side length})\sqrt2$

For the square given in the question,

$\text{Diagonal}=5\sqrt2$

Report an Error

Example Question #13 : Squares

Find the length of the diagonal of a square that has a side length of 159 .

Possible Answers:

159

The length of the diagonal cannot be determined.

$159\sqrt2$

$169\sqrt2$

Correct answer:

$159\sqrt2$

Explanation:

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of the diagonal.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

$\text{Diagonal}=\sqrt{2(\text{side length})^2}$

$\text{Diagonal}=(\text{side length})\sqrt2$

For the square given in the question,

$\text{Diagonal}=159\sqrt2$

Report an Error

Example Question #14 : Squares

Find the length of the diagonal of a square with side lengths of .

Possible Answers:

$27\sqrt2$

$28\sqrt2$

$25\sqrt2$

$9\sqrt2$

Correct answer:

$27\sqrt2$

Explanation:

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of the diagonal.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

$\text{Diagonal}=\sqrt{2(\text{side length})^2}$

$\text{Diagonal}=(\text{side length})\sqrt2$

For the square given in the question,

$\text{Diagonal}=27\sqrt2$

Report an Error

Example Question #15 : Squares

Find the length of the diagonal of a square that has a side length of .

Possible Answers:

$46\sqrt2$

$54\sqrt2$

$23\sqrt2$

Correct answer:

$23\sqrt2$

Explanation:

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of the diagonal.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

$\text{Diagonal}=\sqrt{2(\text{side length})^2}$

$\text{Diagonal}=(\text{side length})\sqrt2$

For the square given in the question,

$\text{Diagonal}=23\sqrt2$

Report an Error

Example Question #16 : Squares

Find the length of the diagonal of a square with side lengths of 122 .

Possible Answers:

$122\sqrt2$

$244\sqrt2$

$61\sqrt2$

122

Correct answer:

$122\sqrt2$

Explanation:

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of the diagonal.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

$\text{Diagonal}=\sqrt{2(\text{side length})^2}$

$\text{Diagonal}=(\text{side length})\sqrt2$

For the square given in the question,

$\text{Diagonal}=122\sqrt2$

Report an Error

Example Question #17 : Squares

Find the length of the diagonal of a square that has side lengths of .

Possible Answers:

$17\sqrt2$

$70\sqrt2$

$35\sqrt2$

Correct answer:

$35\sqrt2$

Explanation:

The diagonal of a square is also a hypotenuse of a right triangle with the side lengths as legs of the triangle.

Use the Pythagorean Theorem to find the length of the diagonal.

$\text{Diagonal}=\sqrt{\text{side length}^2+\text{side length}^2}$

$\text{Diagonal}=\sqrt{2(\text{side length})^2}$

$\text{Diagonal}=(\text{side length})\sqrt2$

For the square given in the question,

$\text{Diagonal}=35\sqrt2$

Report an Error

Example Question #18 : Squares

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

Possible Answers:

$8\sqrt{2}$

$16\sqrt{2}$

Correct answer:

$8\sqrt{2}$

Explanation:

To find the diagonal, you case use the pythagorean theorem or realize that this in isosceles triangle, and therefore the hypotenuse is

$s\sqrt{2}=8\sqrt{2}$

Report an Error

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Basic Geometry : How to find the length of the diagonal of a square

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #11 : Squares

Example Question #261 : Quadrilaterals

Example Question #262 : Quadrilaterals

Example Question #12 : Squares

Example Question #13 : Squares

Example Question #14 : Squares

Example Question #15 : Squares

Example Question #16 : Squares

Example Question #17 : Squares

Example Question #18 : Squares

All Basic Geometry Resources

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