Use an algebraic approach to solve the problem: Suppose that the width of a certain rectangle is 2 inch more than one-fourth of its length. The perimeter of the rectangle is 24 inches. Find the length and width of the rectangle.
A)5 inches wide, 7 inches long
B)2 inches wide, 10 inches long
C)3 inches wide, 9 inches long
D)4 inches wide, 8 inches long
E)7 inches wide, 5 inches long

Question

Quizplus · Accepted Answer

The perimeter of a rectangle is given by $2l + 2w = 24$, where $l$ is the length and $w$ is the width. Given $w = \frac{1}{4}l + 2$, substituting the width's expression into the perimeter equation gives $2l + 2(\frac{1}{4}l + 2) = 24$. Solving this equation for $l$ gives $l = 8$ inches. Substituting $l = 8$ inches back into $w = \frac{1}{4}l + 2$ gives $w = 4$ inches. Therefore, the rectangle is 4 inches wide and 8 inches long.

Use an Algebraic Approach to Solve the Problem: Suppose That