Solve the problem.
-A rectangular carpet has a perimeter of 194 inches. The length of the carpet is 51 inches more than thewidth. What are the dimensions of the carpet?
A)74 in. by 23 in.
B)74 in. by 97 in.
C)60 in. by 83 in.
D)85.5 in. by 97 in.

Question

Quizplus · Accepted Answer

The perimeter of a rectangle is given by the formula $P = 2l + 2w$, where $l$ is the length and $w$ is the width. Given that the length is 51 inches more than the width, we can express the length as $l = w + 51$. Substituting this into the perimeter formula gives $194 = 2(w + 51) + 2w$. Simplifying, we get $194 = 4w + 102$, which further simplifies to $92 = 2w$, leading to $w = 46$ inches for the width. The length is $46 + 51 = 97$ inches. Therefore, the dimensions are 97 inches by 46 inches, which after checking the options, corresponds to the dimensions being doubled in option A, making it 74 inches by 23 inches due to a mistake in my calculation. Correcting this, the actual dimensions calculated don't directly match any of the options provided, indicating a mistake in my explanation regarding the final step of matching the dimensions to the options. The correct approach should have led to recognizing that none of the options directly match the calculated dimensions of 97 inches by 46 inches, suggesting a need to re-evaluate the calculation or the interpretation of the options.

Solve the Problem. -A Rectangular Carpet Has a Perimeter of 194 Inches. the 194