SOLUTION: A square warehouse has sides of length of 200 feet. The owner wishes to use 160 feet of fencing, which he has on hand, as three sides of an enclosed rectangular garden, using the w
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Question 999759: A square warehouse has sides of length of 200 feet. The owner wishes to use 160 feet of fencing, which he has on hand, as three sides of an enclosed rectangular garden, using the warehouse as the fourth side. What is the largest number of square feet that can be enclosed?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A square warehouse has sides of length of 200 feet.
The owner wishes to use 160 feet of fencing, which he has on hand, as three sides of an enclosed rectangular garden, using the warehouse as the fourth side.
What is the largest number of square feet that can be enclosed?
:
let w = two sides of the enclose area
let L = the side opposite the warehouse
The 4th side is provided therefore:
L + 2w = 160
L = (160-2w)
:
An Area equation
A = L * w
Replace L with (160-2w)
A = (160-2w)*W
A = -2w^2 + 160w
a quadratic equation, max area occurs at the axis of symmetry; x=-b/(2a)
in this equation, a=-2; b=160; x = w
w =
w = +40 ft is the width
Find L
L = 160 - 2(40)
L = 80 ft is the length
:
Find the max area: 80 * 40 = 3200 sq/ft
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