Question

A rectangular Persian carpet has a perimeter of 252 inches. The length of the carpet is 28 in, more than the width. What are the dimensions of the carpet?

Answer 1

The length of the carpet is 77 inches and the width is 49 inches.

Explanation:

The formula for perimeter is `p = 2l + 2w` where `p` is the perimeter, `l` is the length and `w` is the width.

If the length of the carpet is 28 in. more than the width we know:

`l = w + 28`

Substituting `w + 28` for `l` and 252 for `p` in the formula for perimeter and solving for `w` while keeping the equation balanced gives:

`252 = 2(w + 28) + 2w`

`252 = 2w + 56 + 2w`

`252 = 4w + 56`

`252 - 56 = 4w + 56 - 56`

`196 = 4w`

`196/4 = (4w)/4`

`w = 49`

And substituting `49` for `w` in the equation for `l` gives:

`l = 49 + 28`

`l = 77`