G.MG.3 Beth is going to enclose a rectangular area in back of her house. The house wall will form one of the four sides of the fenced in area, so Beth will only need to construct three sides of fencing. Beth has 48 feet of fencing. She wants to enclose the maximum possible area.

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raphealnwobi raphealnwobi · Answer 1 · 2022-06-14T19:38:05+02:00

The maximum area of the rectangular path is when the length is 24 feet and the width is 12 feet.

An equation is an expression that shows the relationship between two or more numbers and variables.

Let x represent the length and y represent the width. Hence:

There is 48 feet of fencing:

x + 2y = 48

x = 48 - 2y (1)

The area (A) is:

A = xy = y(48 - 2y)

A = 48y - 2y²

The maximum area is at A' = 0, hence:

48 - 4y = 0

y = 12

x = 48 - 2(12) = 24

The maximum area of the rectangular path is when the length is 24 feet and the width is 12 feet.

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