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

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Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle

A rectangle has a length of 12 in and a width of 5 in. What is the diagonal of the rectangle?

Possible Answers:

$17\; in$

$14\; in$

$16\; in$

$15\; in$

$13\; in$

Correct answer:

$13\; in$

Explanation:

To find the diagonal we use the Pythagorean Theorem:

$5^{2}+12^{2}= x^{2}$ where = hypotenuse

$25+144=x^{2}$ or $x=13\; in$

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Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle

One side of a rectangle is 7 inches and another is 9 inches. How many inches long is the rectangle's diagonal?

Possible Answers:

11.4

130

10.2

Correct answer:

11.4

Explanation:

You can find the diagonal of a rectangle if you have the width and the height. The diagonal equals the square root of the width squared plus the height squared.

$\sqrt{9^{2}+7^{2}}=11.4$

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Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle

Find the length of the diagonal.

Possible Answers:

$4\sqrt{13}$

$16\sqrt{13}$

Correct answer:

$4\sqrt{13}$

Explanation:

The rectangle can be cut into two equal right triangles, where the hypotenuse of both is the rectangle's diagonal.

Use the Pythagorean Theorem to find the hypotenuse:

a^2+b^2=c^2 , where a and b are the legs and c is the hypotenuse

(12)^2 + (8)^2 = c^2

144 + 64 = c^2

208 = c^2

$\sqrt{208} = \sqrt{c^2}$

$c = 4\sqrt{13}$

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Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle

A standard high school basketball court is 84 feet long and 50 feet wide. During practice, Coach K has Kyrie run from one the right corner on one end of the court to the left corner at the other end of the court. To the nearest foot, how far did Kyrie run?

Possible Answers:

98ft

134ft

87ft

104ft

93ft

Correct answer:

98ft

Explanation:

A picture helps greatly with this problem, so we begin with a rectangular basketball court.

We note that the distance run by Kyrie (drawn in red) is the diagonal of our rectangle, which we will call . We should also not that this diagonal divides our rectangle into two congruent right triangles. We can therefore find the length of our diagonal by focusing on one of these triangles and determining the hypotenuse. This can be done with the Pythagorean Theorem, which gives us:

50^2+84^2=k^2

2500+7056=k^2

9556=k^2

Taking the square root gives us

k=97.754795...

Rounding to the nearest foot gives an answer of 98.

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Example Question #2 : How To Find The Length Of The Diagonal Of A Rectangle

A rectangle has a height of and a base of . What is the length of its diagonal rounded to the nearest tenth?

Possible Answers:

28.4

12.2

30.5

24.4

19.5

Correct answer:

24.4

Explanation:

1. Use Pythagorean Theorem with a=14 and b=20 .

$a^{2}+b^{2}=c^{2}$

$14^{2}+20^{2}=c^{2}$

2. Solve for , the length of the diagonal:

$14^{2}+20^{2}=c^{2}$

$196+400=c^{2}$

$596=c^{2}$

c=24.41

This rounds down to 24.4 because the hundredth's place () is less than .

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Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle

The sides of rectangle ABCD are 4 in and 13 in.

How long is the diagonal of rectangle ABCD?

Possible Answers:

185

$\sqrt{125}$

$\sqrt{185}$

Correct answer:

$\sqrt{185}$

Explanation:

A diagonal of a rectangle cuts the rectangle into 2 right triangles with sides equal to the sides of the rectangle and with a hypotenuse that is the diagonal. All you need to do is use the pythagorean theorem:

a^2+b^2=c^2 where a and b are the sides of the rectangle and c is the length of the diagonal.

$\sqrt{4^2+16^2}=\sqrt{185}=c$

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Example Question #2 : How To Find The Length Of The Diagonal Of A Rectangle

Find the length of the diagonal of a rectangle that has a length of and a width of .

Possible Answers:

Correct answer:

Explanation:

The diagonal of a rectangle is also the hypotenuse of a right triangle that has the length and the width of the rectangle as its legs.

We can then use the Pythgorean Theorem to find the diagonal.

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

For the given rectangle,

$\text{Diagonal}=\sqrt{9^2+12^2}=\sqrt{225}=15$

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Example Question #3 : How To Find The Length Of The Diagonal Of A Rectangle

Find the length of the diagonal of a rectangle that has a length of and a width of .

Possible Answers:

Correct answer:

Explanation:

The diagonal of a rectangle is also the hypotenuse of a right triangle that has the length and the width of the rectangle as its legs.

We can then use the Pythgorean Theorem to find the diagonal.

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

For the given rectangle,

$\text{Diagonal}=\sqrt{10^2+24^2}=\sqrt{676}=26$

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Example Question #2 : How To Find The Length Of The Diagonal Of A Rectangle

Find the length of the diagonal of a rectangle that has a length of and a width of .

Possible Answers:

Correct answer:

Explanation:

The diagonal of a rectangle is also the hypotenuse of a right triangle that has the length and the width of the rectangle as its legs.

We can then use the Pythgorean Theorem to find the diagonal.

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

For the given rectangle,

$\text{Diagonal}=\sqrt{6^2+8^2}=\sqrt{100}=10$

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Example Question #10 : How To Find The Length Of The Diagonal Of A Rectangle

Find the length of the diagonal of a rectangle that has a length of and a width of .

Possible Answers:

$6\sqrt{2}$

$4\sqrt3$

$12\sqrt{35}$

$3\sqrt{34}$

Correct answer:

$3\sqrt{34}$

Explanation:

The diagonal of a rectangle is also the hypotenuse of a right triangle that has the length and the width of the rectangle as its legs.

We can then use the Pythgorean Theorem to find the diagonal.

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

For the given rectangle,

$\text{Diagonal}=\sqrt{9^2+15^2}=\sqrt{306}=3\sqrt{34}$

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

Study concepts, example questions & explanations for Basic Geometry

All Basic Geometry Resources

Example Questions

Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #2 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #1 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #2 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #3 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #2 : How To Find The Length Of The Diagonal Of A Rectangle

Example Question #10 : How To Find The Length Of The Diagonal Of A Rectangle

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