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 f enced 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.
1 answer:
The maximum area of the rectangular path is when the length is 24 feet and the width is 12 feet .
<h3>What is an
equation ?</h3>
An equation is an expression that shows the relationship b etween 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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