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?

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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?

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Answer 1 · 2016-11-05T23:48:51

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

Explanation:

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

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

$l = w + 28$ $l = w + 28$

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

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

$252 = 2 w + 56 + 2 w$ $252 = 2w + 56 + 2w$

$252 = 4 w + 56$ $252 = 4w + 56$

$252 - 56 = 4 w + 56 - 56$ $252 - 56 = 4w + 56 - 56$

$196 = 4 w$ $196 = 4w$

$\frac{196}{4} = \frac{4 w}{4}$ $196/4 = (4w)/4$

$w = 49$ $w = 49$

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

$l = 49 + 28$ $l = 49 + 28$

$l = 77$ $l = 77$

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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?

1 Answer

Explanation:

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