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)

Question

Mathematics

Dalia Avery

24 September, 10:37

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)

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Answers (1)

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Koen Powers · Answer 1

m=21 and n=21

Step-by-step 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.