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

Study concepts, example questions & explanations for Basic Geometry

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9 Diagnostic Tests 164 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #304 : Squares

If the diagonal of a square is $55\sqrt2$ , what is the length of one side of the square?

Possible Answers:

$45\sqrt2$

$55\sqrt2$

$\frac{55}{\sqrt2}$

Correct answer:

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.

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

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

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

$\text{Side length}=\frac{\text{Diagonal}}{\sqrt2}$

For the square given in the question,

$\text{Side length}=\frac{55\sqrt2}{\sqrt{2}}$

Simplify.

$\text{Side length}=55$

Report an Error

Example Question #42 : How To Find The Length Of The Side Of A Square

If the diagonal of a square is $16\sqrt2$ , what is the length of one side of the square?

Possible Answers:

Correct answer:

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.

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

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

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

$\text{Side length}=\frac{\text{Diagonal}}{\sqrt2}$

For the square given in the question,

$\text{Side length}=\frac{16\sqrt2}{\sqrt{2}}$

Simplify.

$\text{Side length}=16$

Report an Error

Example Question #43 : How To Find The Length Of The Side Of A Square

If the diagonal of a square is $27\sqrt2$ , what is the length of one side of the square?

Possible Answers:

Correct answer:

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.

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

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

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

$\text{Side length}=\frac{\text{Diagonal}}{\sqrt2}$

For the square given in the question,

$\text{Side length}=\frac{27\sqrt2}{\sqrt{2}}$

Simplify.

$\text{Side length}=27$

Report an Error

Example Question #44 : How To Find The Length Of The Side Of A Square

If the diagonal of a square is $10\sqrt2$ , what is the length of one side of the square?

Possible Answers:

Correct answer:

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.

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

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

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

$\text{Side length}=\frac{\text{Diagonal}}{\sqrt2}$

For the square given in the question,

$\text{Side length}=\frac{10\sqrt2}{\sqrt{2}}$

Simplify.

$\text{Side length}=10$

Report an Error

Example Question #961 : Basic Geometry

If the diagonal of a square is $9\sqrt2$ , what is the length of one side of the square?

Possible Answers:

$9\sqrt2$

$18\sqrt2$

Correct answer:

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.

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

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

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

$\text{Side length}=\frac{\text{Diagonal}}{\sqrt2}$

For the square given in the question,

$\text{Side length}=\frac{9\sqrt2}{\sqrt{2}}$

Simplify.

$\text{Side length}=9$

Report an Error

Example Question #312 : Squares

If the diagonal of a square is $88\sqrt2$ , what is the length of one side of the square?

Possible Answers:

176

$88\sqrt2$

$44\sqrt2$

Correct answer:

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.

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

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

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

$\text{Side length}=\frac{\text{Diagonal}}{\sqrt2}$

For the square given in the question,

$\text{Side length}=\frac{88\sqrt2}{\sqrt{2}}$

Simplify.

$\text{Side length}=88$

Report an Error

Example Question #961 : Basic Geometry

If the diagonal of a square is $97\sqrt2$ , what is the length of one side of the square?

Possible Answers:

157

196

Correct answer:

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.

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

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

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

$\text{Side length}=\frac{\text{Diagonal}}{\sqrt2}$

For the square given in the question,

$\text{Side length}=\frac{97\sqrt2}{\sqrt{2}}$

Simplify.

$\text{Side length}=97$

Report an Error

Example Question #561 : Quadrilaterals

If the diagonal of a square is , what is the length of one side of the square?

Possible Answers:

$12\sqrt2$

$6\sqrt2$

Correct answer:

$6\sqrt2$

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.

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

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

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

$\text{Side length}=\frac{\text{Diagonal}}{\sqrt2}$

For the square given in the question,

$\text{Side length}=\frac{12}{\sqrt{2}}$

Multiply the top and bottom of the fraction by one in the form of $\frac{\sqrt{2}}{\sqrt{2}}$

$\text{Side length}=\frac{12}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}$

Solve.

$\text{Side length}=\frac{12\sqrt2}{2}$

Simplify.

$\text{Side length}=6\sqrt2$

Report an Error

Example Question #972 : Basic Geometry

If the diagonal of a square is , what is the length of one side of the square?

Possible Answers:

$10\sqrt2$

$5\sqrt2$

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.

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

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

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

$\text{Side length}=\frac{\text{Diagonal}}{\sqrt2}$

For the square given in the question,

$\text{Side length}=\frac{10}{\sqrt{2}}=\frac{10\sqrt2}{2}=5\sqrt2$

Multiply the top and bottom of the fraction by one in the form of $\frac{\sqrt{2}}{\sqrt{2}}$

$\text{Side length}=\frac{10}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}$

Silve.

$\text{Side length}=\frac{10\sqrt2}{2}$

Simplify.

$\text{Side length}=5\sqrt2$

Report an Error

Example Question #311 : Squares

Given that the area of a square is 16 cm^2 , solve for the lengths of the sides.

Possible Answers:

7cm

3cm

8cm

4cm

9cm

Correct answer:

4cm

Explanation:

To find the answer to this question, the formula for area is needed.

Area = Side(Side)

Plugging in the numbers, we get:

16 = Side (Side)

This is also written as

16 = Side^2

Take the sqare root of 16, and you get:

4cm = side

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

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #304 : Squares

Example Question #42 : How To Find The Length Of The Side Of A Square

Example Question #43 : How To Find The Length Of The Side Of A Square

Example Question #44 : How To Find The Length Of The Side Of A Square

Example Question #961 : Basic Geometry

Example Question #312 : Squares

Example Question #961 : Basic Geometry

Example Question #561 : Quadrilaterals

Example Question #972 : Basic Geometry

Example Question #311 : Squares

All Basic Geometry Resources

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