Question

A rectangular carpet has a perimeter of 234 inches. The length of the carpet is 83 inches more than the width. What are the dimensions of the carpet?

Answer 1

Answer:

Perimeter = 2 x length + 2 x width

Width = x

Length = x + 71

234 = 2*(x + 71) + 2*(x)

234 = 2x + 142 + 2x

234 = 4x + 142

4x = 234 - 142

4x = 92

x = 23

Width = 23 inches

Length = 94 inches

Step-by-step explanation:

Answer 2

The dimensions of the rectangular carpet are 100 and 17 inches.

• Let the length of the rectangle be L.

• Let the width of the rectangle be W.

Given the following data:

• Perimeter = 234 inches

Translating the word problem into an algebraic equation, we have;

$L = W + 83$

To find the dimensions of the rectangular carpet;

Mathematically, the perimeter of a rectangle is given by the formula;

$Perimeter = 2(L+W)$

Substituting the values into the formula, we have;

$234 = 2(W + 83 + W)$

$234 = 2(2W + 83)\\\\234 = 4W + 166\\\\4W = 234 - 166\\\\4W = 68\\\\W = \frac{68}{4}$

Width, W = 17 inches

Next, we would find the value of L;

$L = W + 83$

Substituting the value of W, we have;

$L = 17 + 83$

L = 100 inches.

Therefore, the dimensions of the rectangular carpet are 100 and 17 inches.

Find more information: brainly.com/question/897975