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

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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) About Me  (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 ax%5E2%2Bbx%2Bc=0 (in our case -2x%5E2%2B26x%2B-72+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2826%29%5E2-4%2A-2%2A-72=100.

Discriminant d=100 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-26%2B-sqrt%28+100+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2826%29%2Bsqrt%28+100+%29%29%2F2%5C-2+=+4
x%5B2%5D+=+%28-%2826%29-sqrt%28+100+%29%29%2F2%5C-2+=+9

Quadratic expression -2x%5E2%2B26x%2B-72 can be factored:
-2x%5E2%2B26x%2B-72+=+-2%28x-4%29%2A%28x-9%29
Again, the answer is: 4, 9. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2%2Ax%5E2%2B26%2Ax%2B-72+%29

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