SOLUTION: A rectangular plot of ground is to be enclosed by a fence then divided down the middle by another fence. If the fence down the middle costs $3 and the rest of the fencing costs $5.

Question 1078284: A rectangular plot of ground is to be enclosed by a fence then divided down the middle by another fence. If the fence down the middle costs $3 and the rest of the fencing costs $5. find the dimensions of the plot of the largest possible area that can be fenced for $130
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A rectangular plot of ground is to be enclosed by a fence then divided down the middle by another fence.
If the fence down the middle costs $3 and the rest of the fencing costs $5. find the dimensions of the plot of the largest possible area that can be fenced for $130.
:
let L = the length of the plot
let w = the width of the plot
:
5(2L) + 5(2w) + 3w = 130
10L + 10w + 3w = 130
10L + 13w = 130
10L = -13w + 130
L = w + 13
L = -1.3w + 13
:
Area
A = L * w
replace L with (-1.3w+13)
A = (-1.3w + 13)*w =
A = -1.3w^2 + 13w
A quadratic equation. Max area occurs on the axis of symmetry (x=-b/2a)
w =
w =
w = 5 meters is the width for max area
then
L = -1.3(5) + 13
L = -6.5 + 13
L = 6.5 meters is the length for max area
:
Max area = 5 * 6.5 = 32.5 sq meters

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