High School Math : How to find the length of the diagonal of a rectangle

Study concepts, example questions & explanations for High School Math

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Example Questions

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

What is the diagonal of a rectangle with a side length of 5 and a base of 8? (Round to the nearest tenth)

Possible Answers:

Correct answer:

Explanation:

To find the diagonal of a rectangle we must use the side lengths to create a 90 degree triangle with side lengths of 5, 8, and a hypotenuse which is equal to the diagonal.

If we have a right angle triangle and a value for two of the three side lengths, we use the Pythagorean Theorem to solve for the length of the third side.

The two side lengths that meet to form the right angle are labeled  and  which are interchangeable for each side length.

The long length connecting them is labeled  and is known as the hypotenuse.

The Pythagorean Theorem states 

Take 5 and 8 and plug them into the equation as  and  to yield 

First square the numbers 

After squaring the numbers add them together 

Once you have the sum, square root both sides 

After calculating our answer for the diagonal is .

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

What is the length of the diagonal of a rectangle that is 3 feet long and 4 feet wide?

Possible Answers:

6\ feet

5\ feet

4\ feet

8\ feet

7\ feet

Correct answer:

5\ feet

Explanation:

The diagonal of the rectangle is equivalent to finding the length of the hypotenuse of a right triangle with sides 3 and 4. Using the Pythagorean Theorem:

3^{2}+4^{2} = hypotenuse^{2}

25 = hypotenuse^{2}

hypotenuse = 5

Therefore the diagonal of the rectangle is 5 feet.

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

The length and width of a rectangle are in the ratio of 3:4. If the rectangle has an area of 108 square centimeters, what is the length of the diagonal?

Possible Answers:

9 centimeters

15 centimeters

18 centimeters

12 centimeters

24 centimeters

Correct answer:

15 centimeters

Explanation:

The length and width of the rectangle are in a ratio of 3:4, so the sides can be written as 3x and 4x.

We also know the area, so we write an equation and solve for x:

(3x)(4x) = 12x= 108.

x2 = 9

x = 3

Now we can recalculate the length and the width:

length = 3x = 3(3) = 9 centimeters

width = 4x = 4(3) = 12 centimeters

Using the Pythagorean Theorem we can find the diagonal, c:

length2 + width2 = c2

92 + 12= c2 

81 + 144 = c2

225 = c2

= 15 centimeters

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