The perimeter of a rectangle is 32 centimeters and the area is 48 square centimeters. Find the length and width of the rectangle.
A) 6 cm, 10 cm
B) 4 cm, 12 cm
C) 3 cm, 11 cm
D) 3 cm, 13 cm

Question

Quizplus · Accepted Answer

Let the length of the rectangle be $l$ and the width be $w$. We know that $2(l+w) = 32$, or $l + w = 16$, and that $lw = 48$. We can solve for $w$ in the second equation to get $w = \frac{48}{l}$. We can substitute this into the first equation to get $l + \frac{48}{l} = 16$. Multiplying both sides by $l$ gives us $l^2+48=16l$, which we can rearrange to $l^2-16l+48=0$. Factoring gives us $(l-4)(l-12) = 0$, so $l=4$ or $l=12$. We can check that $w$ is positive in both cases, so the dimensions of the rectangle are either 4 cm by 12 cm or 12 cm by 4 cm. Since the question asks for the length and width of the rectangle, not the other way around, the answer is $B$: 4 cm, 12 cm.

The Perimeter of a Rectangle Is 32 Centimeters and the Area