SOLUTION: Marie made a rectangular pen for her dog using a side of the barn for one side and 26 m of fencing for the remaining 3 sides. If the area enclosed was 72 m squared, find the dimens

Question 952212: Marie made a rectangular pen for her dog using a side of the barn for one side and 26 m of fencing for the remaining 3 sides. If the area enclosed was 72 m squared, find the dimensions of the pen.
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
x=length perpendicular to wall; y=length parallel to wall
2x+y=26m
y=26m-2x
x*y=72sq m
x(26m-2x)=72sq m
-2x^2+26x=72 sq m
-2x^2+26x-72=0

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=100 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 4, 9. Here's your graph:

ANSWERS: x=4 m or x=9m
For x=4 m:
y=26m-2x=26m-8m=18m For x=4m, y=18m
For x=9 m:
y=26m-2x=26m-18m=8m For x=9m, y=8m
CHECK
(4m,18m):
A=x*y
72 sq m=4m*18m
72 sq m=72 sq m
(9m,8m)
A=x*y
72 sq m=8m*9m
72 sq m=72 sq m
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