SOLUTION: you have 100 feet of fencing for a garden to be built along the long wall at the back of your yard. what are the dimensions of the largest garden that can be enclosed by this fenci

Algebra ->  Rectangles -> SOLUTION: you have 100 feet of fencing for a garden to be built along the long wall at the back of your yard. what are the dimensions of the largest garden that can be enclosed by this fenci      Log On


   

Question 497045: you have 100 feet of fencing for a garden to be built along the long wall at the back of your yard. what are the dimensions of the largest garden that can be enclosed by this fencing?
Answer by cleomenius(959) About Me  (Show Source):
You can put this solution on YOUR website!
The perimeter of the rectangle is
2W + 2 L
Because there are only 3 sides, the perimeter will be
P = 2W + L
100 = 2W + L
Now, rearrange for length
L = 100 = 2W
Now the area formula:
A = L*W
=========================
Area = W(100 - 2W)
Area = 100x -2x^2
This becomes a quadratic equation:
-2W^2 + 100W
===================================
Find the max area width by finding the axis of symmetry;
W = -b/(2a)
a= -2
b = 100
W = -100 / -4
W = 25 feet. This is the width.
L = 100 - 2W = 50 feet. This is the length.
25 * 50 = 1250 ft, this is the maximum area.
Cleomenius.