Among all rectangles that have a perimeter of 176, find the dimensions of the one whose area is largest. write your answers as fractions reduced to lowest terms.

Question

Mathematics

Addison Kirby

25 July, 16:32

Among all rectangles that have a perimeter of 176, find the dimensions of the one whose area is largest. write your answers as fractions reduced to lowest terms.

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Answers (2)

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Azul Cervantes · Answer 1

To get the largest area, the length and the width have to be as close as possible, if not the same.

Given Perimeter = 176 unit.

Length = 176 : 4 = 44 units

Area = Length x Width

Area = 44 x 44 = 1936 units²

1936 units² is the largest possible area, given that the perimeter is 176 units. The dimension being 44 by 44

Kaliyah Alvarez · Answer 2

Th rectangle whose area is largest is a square. So the dimensions of a rectangle with maximum area is 176 / 4 = 44

Dimensions are 44 * 44.