For a rectangle with perimeter 32 to have the largest area, what dimensions should it have ?
A) $8 \times 7$
B) $16 \times 16$
C) $7 \times 9$
D) $8 \times 8$
E) $8 \times 9$

Question

For a rectangle with perimeter 32 to have the largest area, what dimensions should it have  ?
A) $8 \times 7$
B) $16 \times 16$
C) $7 \times 9$
D) $8 \times 8$
E) $8 \times 9$

Quizplus · Accepted Answer

For a rectangle, the largest area for a given perimeter is achieved when the rectangle is a square. The perimeter of a rectangle is given by $2l + 2w = 32$, where $l$ and $w$ are the length and width of the rectangle, respectively. For a square, $l = w$, so $4l = 32$, leading to $l = 8$. Therefore, an $8 \times 8$ square has the largest area among the given options.

For a Rectangle with Perimeter 32 to Have the Largest 8×78 \times 78×7

For a Rectangle with Perimeter 32 to Have the Largest $8 \times 7$