ACT Math : How to find the length of the diagonal of a rectangle

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #4 : 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:

Correct answer:

Explanation:

1. Use Pythagorean Theorem with  and .

 

2. Solve for , the length of the diagonal:

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

Example Question #5 : 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:

Correct answer:

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:

 where a and b are the sides of the rectangle and c is the length of the diagonal. 

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

A power company needs to run a piece of wire across a rectangular plot of land and must do so diagonally.  The land is   by   in measurement. If it costs   for each mile of wire deployed, how much is the expected cost of this project?  Round to the nearest cent.

Possible Answers:

Correct answer:

Explanation:

Notice that this problem could be represented as follows:

Rect62

This means that you can find the distance of the wire merely by using the Pythagorean theorem:

Solving for , you get:

Thus, 

Using your calculator, multiply this by .  This gives you approximately  dollars in expenses.

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

What is the diagonal of a rectangle with sides of length  and ? Round to the nearest hundredth.

Possible Answers:

Correct answer:

Explanation:

You could draw this rectangle as follows:

Rect212

Solving for the diagonal merely requires using the Pythagorean theorem. Thus, you know:

 or 

, meaning that 

This is approximately  Thus, the answer is .

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

What is the area of a rectangle with a diagonal of   and one side that is  ?

Possible Answers:

 

 

 

 

 

Correct answer:

 

Explanation:

Based on the description offered in the question, you know that your rectangle must look something like this:

Rect15hyp

Using the Pythagorean theorem, you can solve for the unknown side :

Thus,  is .  This means that the area is  or  .

Example Question #4 : How To Find The Length Of The Diagonal Of A Rectangle

Mark bought a TV at the store that was listed as 36in x 24in. He needs to figure out the diagonal to make sure the television is large enough but he left his measuring tape at his mother's house. What is the diagonal length of this television's screen in terms of inches?

Possible Answers:

Correct answer:

Explanation:

Finding the diagonal of a rectangle is essentially a problem with triangles. If we set up a right triangle with legs 24 in. and 36 in., and set  to be the diagonal (the hypotenuse), we can use the Pythagorean Theorem to solve for :

This comes out to be about 43.3 in.

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