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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

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All Basic Geometry Resources

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

Example Questions

Example Question #38 : How To Find The Length Of The Side Of A Square

If the diagonal of a square is $2\sqrt2$ , what is the length of one side of the square?

Possible Answers:

$2\sqrt2$

$\sqrt2$

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,

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

Simplify.

$\text{Side length}=2$

Report an Error

Example Question #39 : How To Find The Length Of The Side Of A Square

If the diagonal of the square is $4\sqrt2$ , what is the length of one side of the square?

Possible Answers:

$4\sqrt2$

$2\sqrt2$

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,

$\text{Side length}=\frac{4\sqrt2}{\sqrt{2}}$

Simplify.

$\text{Side length}=4$

Report an Error

Example Question #40 : How To Find The Length Of The Side Of A Square

If the diagonal of a square is $12\sqrt2$ , 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,

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

Simplify.

$\text{Side length}=12$

Report an Error

Example Question #553 : Quadrilaterals

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 #554 : Quadrilaterals

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 #555 : Quadrilaterals

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 #556 : Quadrilaterals

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 #41 : How To Find The Length Of The Side Of A Square

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

Possible Answers:

$18\sqrt2$

$9\sqrt2$

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

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

Possible Answers:

$44\sqrt2$

176

$88\sqrt2$

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 #311 : Squares

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

Possible Answers:

196

157

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

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All Basic Geometry Resources

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Basic Geometry : Plane Geometry

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #38 : How To Find The Length Of The Side Of A Square

Example Question #39 : How To Find The Length Of The Side Of A Square

Example Question #40 : How To Find The Length Of The Side Of A Square

Example Question #553 : Quadrilaterals

Example Question #554 : Quadrilaterals

Example Question #555 : Quadrilaterals

Example Question #556 : Quadrilaterals

Example Question #41 : How To Find The Length Of The Side Of A Square

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

Example Question #311 : Squares

All Basic Geometry Resources

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