SOLUTION: The director of the Glen Island Zoo wants to use 170m of fencing to enclose a petting area of 1750m squared. Find the dimensions of the petting zoo.

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Question 433187: The director of the Glen Island Zoo wants to use 170m of fencing to enclose a petting area of 1750m squared. Find the dimensions of the petting zoo.
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
In order for this to work:
2x+2y=170
xy=1750
-----------------
y=1750/x
2x+2(1750/x)=170
2x+3500/x=170
2x2+3500=170x
2x2-170x+3500=0
x2-85x+1750=0
(x-35)(x-50)=0
x=35,50
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Thus a petting zoo of 35m X 50m would work perfectly.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-85x%2B1750+=+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=%28-85%29%5E2-4%2A1%2A1750=225.

Discriminant d=225 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--85%2B-sqrt%28+225+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-85%29%2Bsqrt%28+225+%29%29%2F2%5C1+=+50
x%5B2%5D+=+%28-%28-85%29-sqrt%28+225+%29%29%2F2%5C1+=+35

Quadratic expression 1x%5E2%2B-85x%2B1750 can be factored:
1x%5E2%2B-85x%2B1750+=+1%28x-50%29%2A%28x-35%29
Again, the answer is: 50, 35. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-85%2Ax%2B1750+%29