The width of the carpet is 33 inches and the length is 61 inches
From the question,
We are to determine the width and length of the rectangular carpet.
Let the width be w and the length be l
From the first statement
A rectangular Persian carpet has a perimeter of 188 inches.
The perimeter of a rectangle is given by
P = 2(l +w)
∴ 188 = 2(l +w) ----------- (1)
From the second statement
The length of the carpet is 28 inches more than the width
That is,
l = 28 + w ---------- (2)
Substitute equation (2) into equation (1)
188 = 2(l +w)
We get
188 = 2(28 +w +w)
This becomes,
188 = 2 (28 +2w)
188 = 56 + 4w
Subtract 56 from both sides
188 - 56 = 56 - 56 + 4w
132 = 4w
∴ w = 132÷4
w = 33 inches
Now, substitute the value of w into equation (2) to get l
l = 28 + w
We get
l = 28 + 33
l = 61 inches
Hence, the width of the carpet is 33 inches and the length is 61 inches
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