a rectangularpersian carpet has a perimeter of 208 inches. the length of the carpet is 30 inches more than the width, what are the dimensions of the carpet?

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2 Answers

Perimeter = 2Width + 2Length, or 208 = 2W + 2L

L = W + 30, plug into above equation --> 208 = 2W + 2(W+30)

Expand: 208 = 2W + 2W + 30

Combine like terms: 178 = 4W --> W = 44.5 in.

Solve for L: L = 44.5 + 30 --> L = 74.5 in.

Victoria B. 12/16/2012

Comments

Good answer Victoria, but you forgot to multiply the 30 by 2 (in the second line). Your length and width give a perimeter of 238 inches.

- Daniel O. 12/17/2012

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Actually, I think Victoria's answer is incorrect.

Her method is correct, but her solution doesn't work:

Given that the perimeter is twice the length plus twice the width, and the length is 30 inches longer than the width, we can indeed make an equation as follows:

2L + 2W = 208 and since L = W + 30, 2 (W + 30) + 2W = 208

Here is the first way to do it: 2 (W + 30) = 2W + 60, so 2 (W + 30) + 2W = 4W +60

so 4W + 60 = 208 subtract 60 from each side

4W = 148 divide each side by 4

W = 37

And since L = W + 30, L = 67

And now, to check our work, 2L = 67 * 2 = 134

2W = 37 * 2 = 74

So the perimeter which is twice the length plus twice the width = 2L + 2W = 134 + 74 = 208.

Maurice S. 12/16/2012