SOLUTION: A water pipe runs diagonally under a rectangular garden that is 7 feet longer then it is wide. If the pipe is 13 feet long, what are the dimensions of the garden

Algebra ->  Pythagorean-theorem -> SOLUTION: A water pipe runs diagonally under a rectangular garden that is 7 feet longer then it is wide. If the pipe is 13 feet long, what are the dimensions of the garden       Log On


   

Question 447083: A water pipe runs diagonally under a rectangular garden that is 7 feet longer then it is wide. If the pipe is 13 feet long, what are the dimensions of the garden
Answer by chriswen(106) About Me  (Show Source):
You can put this solution on YOUR website!
Let x ft be the width of the garden.
Let x+7 ft be the length of the garden.
...
%28x%29%5E2%2B%28x%2B7%29%5E2=13%5E2 ... Pythagorean theorem
x%5E2%2Bx%5E2%2B14x%2B49=169
2x%5E2%2B14x%2B49-169=0
2x%5E2%2B14x-120=0
2%28x%5E2%2B7x-60%29=0
x%5E2%2B7x-60=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B7x%2B-60+=+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=%287%29%5E2-4%2A1%2A-60=289.

Discriminant d=289 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+289+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%287%29%2Bsqrt%28+289+%29%29%2F2%5C1+=+5
x%5B2%5D+=+%28-%287%29-sqrt%28+289+%29%29%2F2%5C1+=+-12

Quadratic expression 1x%5E2%2B7x%2B-60 can be factored:
1x%5E2%2B7x%2B-60+=+1%28x-5%29%2A%28x--12%29
Again, the answer is: 5, -12. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B7%2Ax%2B-60+%29

x must be positive.
x=5
x+7=12
Therefore, the dimensions of the garden is 5 ft by 12 ft.