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.

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

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fichoh fichoh · Answer 2 · 2021-10-19T11:15:48+02:00

Of all rectangles with a perimeter of 176 units, the rectangle with the largest area would have an area of 1936 unit²

Recall :

Area of a rectangle = Length × width

The rectangle with the largest area value would have the length of the sides almost of equal value, hence, we can approximate the length and width of such rectangle thus :

Length of sides = Perimeter / number of sides
Length of sides = 176 / 4 = 44 units
The length and width will be almost equal to this value.

Therefore, the area would be (length × width) = (44 × 44) = 1936 unit²

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