The width of a rectangle is 18 inches less than $\frac { 1 } { 8 }$ of its length. If the perimeter of the rectangle 342 inches, find the area of the rectangle.
A) $504 \mathrm { in } ^ { 2 }$
B) $168 \text { in } ^ { 2 }$
C) $252 \mathrm { in } ^ { 2 }$
D) $3 \text { in } ^ { 2 }$

Question

Quizplus · Accepted Answer

Let the length of the rectangle be $L$ inches and the width be $W$ inches. According to the problem, $W = \frac{1}{8}L - 18$. The perimeter of a rectangle is given by $2(L + W) = 342$ inches. Substituting $W$ from the first equation into the perimeter equation gives $2\left(L + \frac{1}{8}L - 18\right) = 342$. Simplifying, we get $L + \frac{1}{8}L = 171 + 18$, which simplifies further to $\frac{9}{8}L = 189$. Solving for $L$ gives $L = 168$ inches. Substituting $L$ back into the equation for $W$ gives $W = \frac{1}{8}(168) - 18 = 21 - 18 = 3$ inches. Therefore, the area of the rectangle, which is $L \times W$, is $168 \times 3 = 504 \text{ in}^2$.

The Width of a Rectangle Is 18 Inches Less Than 18\frac { 1 } { 8 }81​

The Width of a Rectangle Is 18 Inches Less Than $\frac { 1 } { 8 }$