Question

Find the dimensions of a rectangle with perimeter 84 m whose area is as large as possible. (If both values are the same number, enter it into both blanks.) m (smaller value) m (larger value)

Answer 1

Length = Breadth = 21m

Explanation:

(see attached)

Answer 2

m=21 and n=21

Explanation:

In order to maximize the area of the rectangle, you want the two side lengths to be as equal to each other as possible.

In this case, we get that 2m+2n=84, so m+n=42. In our case, m and n can equal each other, so that gives us the maximum area of 441

Proof that this works:

If we had other dimensions, like m=20 and n=22, the area would be 440, slightly less than 442. If m=19 and n=23, the area becomes 437, which is even further off from 441.