SOLUTION: The length of a reactangle is 5 meters more than twice its width, and the area of the rectangle is 88 meters squared. Find the dimensions of the rectangle.

Algebra ->  Rectangles -> SOLUTION: The length of a reactangle is 5 meters more than twice its width, and the area of the rectangle is 88 meters squared. Find the dimensions of the rectangle.      Log On


   

Question 310500: The length of a reactangle is 5 meters more than twice its width, and the area of the rectangle is 88 meters squared. Find the dimensions of the rectangle.
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
A=LW
A=88
88=LW
L=5+2W
88=%285%2B2W%29W
88=5W%2B2W%5E2
0=2W%5E2%2B5W-88
view below for quadratic formula explanation
W=5.5 has to be positive
L=5%2B2%285.5%29
L=16
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aW%5E2%2BbW%2Bc=0 (in our case 2W%5E2%2B5W%2B-88+=+0) has the following solutons:

W%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=%285%29%5E2-4%2A2%2A-88=729.

Discriminant d=729 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+729+%29%29%2F2%5Ca.

W%5B1%5D+=+%28-%285%29%2Bsqrt%28+729+%29%29%2F2%5C2+=+5.5
W%5B2%5D+=+%28-%285%29-sqrt%28+729+%29%29%2F2%5C2+=+-8

Quadratic expression 2W%5E2%2B5W%2B-88 can be factored:
2W%5E2%2B5W%2B-88+=+2%28W-5.5%29%2A%28W--8%29
Again, the answer is: 5.5, -8. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B5%2Ax%2B-88+%29