Question

The perimeter of a rectangle is 56 feet. What are the dimensions of the rectangle with maximum area?

Answer 1

14 by 14 ft

Explanation:

perimeter: 4(14) = 56 ft

area: 14(14) = 196 ft ^2

Answer 2

the perimeter of a rectangle is 56 yards. what are the dimensions of the rectangle with maximum area?

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let x=length

let y=width

2x+2y=56

x+y=28

y=28-x

Area=xy=x(28-x)=28x-x^2

Area=-x^2+28x

complete the square:

Area=-(x^2-28x+196)+196

=-(x-14)^2+196

This is an equation of a parabola that opens downward with vertex at (14,196), which means maximum area of 196 occurs when x, the length=14)

dimensions of the rectangle with maximum area? 14 yds by 14 yds, a square.