SOLUTION: The length of a field is 200ft longer than it is wide. The area of the field is 57,600 sq. ft. What is the width of the field?

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Question 963414: The length of a field is 200ft longer than it is wide. The area of the field is 57,600 sq. ft. What is the width of the field?
Answer by amarjeeth123(569) About Me  (Show Source):
You can put this solution on YOUR website!
Let the width be x.
Then the length is (x+200)
The area of the field=57600
Area=length*width
x(x+200)=57600
x^2+200x-57600=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B200x%2B-57600+=+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=%28200%29%5E2-4%2A1%2A-57600=270400.

Discriminant d=270400 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-200%2B-sqrt%28+270400+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28200%29%2Bsqrt%28+270400+%29%29%2F2%5C1+=+160
x%5B2%5D+=+%28-%28200%29-sqrt%28+270400+%29%29%2F2%5C1+=+-360

Quadratic expression 1x%5E2%2B200x%2B-57600 can be factored:
1x%5E2%2B200x%2B-57600+=+1%28x-160%29%2A%28x--360%29
Again, the answer is: 160, -360. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B200%2Ax%2B-57600+%29

x=160 or x=-360
The width of the field is 160 feet.