Find the length and width of a rectangle that has perimeter $32$ meters and a maximum area.
A)4, 12
B)1, 15
C)8, 8
D)9, 7
E)12, 4

Question

Quizplus · Accepted Answer

For a given perimeter, a rectangle has the maximum area when it is a square. The perimeter of a rectangle is given by $2l + 2w = 32$, where $l$ is the length and $w$ is the width. For a square, $l = w$, so $4l = 32$, leading to $l = 8$. Therefore, the dimensions that give the maximum area are $8$ meters by $8$ meters.

Find the Length and Width of a Rectangle That Has 323232

Find the Length and Width of a Rectangle That Has $32$