Question

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9) A rectangular Persian carpet has a perimeter of 240 inches. The length of the carpet is 30 inches
more than the width. What are the dimensions of the carpet?
A) 105 in., 135 in. B) 90 in., 120 in. C) 75 in., 105 in. D) 45 in., 75 in.​

Answer 1

D) 45 in., 75 in

Explanation:

A rectangle with width w and length l has the perimeter given by the following equation:

`P = 2w + 2l`

A rectangular Persian carpet has a perimeter of 240 inches.

This means that
`2w + 2l = 240`

Simplifying by 2

`w + l = 120`

The length of the carpet is 30 inches more than the width.

This means that
`l = 30 + w`

So

`w + l = 120`

`w + 30 + w = 120`

`2w + 30 = 120`

`w = 45`

`l = 30 + w = 30 + 45 = 75`

So the correct answer is:

D) 45 in., 75 in