Question

A rectangular persian carpet has a perimeter of 176 inches. the length of the carpet is 20 inches more than the width. what are the dimensions of the carpet?

Answer 1

The detentions of the carpet are: 34" X 54"

Explanation:

y = width of the carpet

The Length: 20+y

The Perimeter: 2(l+w) -length and width-

176 = 2(y+20+y)

176/2 = 2y + 20

88 - 20 = 2y

68/2 = y

34” = y

Length: 20+34 = 54

Dimensions: 34 X 54

Answer 2

We first need to express this problem as an equation. We'll begin with the formula for perimeter:

2L + 2W = P

Insert any known values:

2L + 2W = 176

Because the carpet is rectangular, the two longer sides are equal in length and the two shorter sides are equal in length. The width can be expressed simply as "x" inches. Insert this variable into the equation:

2L + 2x = 176

The length depends directly on the value of the width. We know from the information given in the problem that the length is equal to the value of the carpet plus 20 inches. This can be expressed using the previously determined variable of width:

L = x + 20

Insert this known value into the equation and simplify:

2(x + 20) + 2x = 176
2x + 40 + 2x = 176
40 + 4x = 176

Now solve for "x." Start by subtracting 40 from both sides of the equation:

4x = 136

Divide 4 from both sides:

x = 34

We have now proven that "x" is equal to 34. Because the width was equal to "x" inches, we have also proven that the width is equal to 34 inches. To find the value of the length, insert the known value of "x" into the equation for L and simplify:

L = x + 20
L = 34 + 20
L = 54

We have now proven that the length is equal to 54 inches.

The correct dimensions of the carpet are in bold.

I hope this helps!