Find the dimensions of a rectangle with perimeter 116 m whose area is as large as possible. (if both values are the same number, enter it into both blanks.)

Question

Mathematics

Martha Nash

3 May, 16:01

Find the dimensions of a rectangle with perimeter 116 m whose area is as large as possible. (if both values are the same number, enter it into both blanks.)

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Peyton Santiago · Answer 1

The dimensions would be 29 by 29.

To maximize area and minimize perimeter, we make the dimensions as close to equilateral as possible.

Dividing the perimeter by the number of sides, we have

116/4 = 29

This means that both length and width can be 29.