College Algebra Homework

Question

A gardener has 440 feet of fencing to fence in a rectangular garden. One side of the garden is bordered by a river and so it does not need any fencing.

What dimensions would guarantee that the garden has the greatest possible area? 

shorter side: ft

longer side: ft

Greatest possible area: ft² 

Answer 1

Let x = width

Let y= length

Area = xy

Perimeter = x+x+y Plug in known values

440=2x+y Solve for y

y=440-2x Plug this into the area equation

Area = x(440-2x) Distribute

Area = 440x-2x² Reorder the terms

Area = -2x²+440x

The max occurs at the vertex.

x coordinate of the vertex = -b/2a = -440/[2*(-2)] = 110 ft = x

y=440-2x = 440-2(110) = 220 ft = y

Max area = xy = (110)(220) = 24200 ft² = Max area