SOLUTION: the length of a rectangle is 6 centimeters less than four times its width. If the area is 40 square centimeters, find the length and width.

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Question 614333: the length of a rectangle is 6 centimeters less than four times its width. If the area is 40 square centimeters, find the length and width.
Answer by asuar010(338) About Me  (Show Source):
You can put this solution on YOUR website!
the width is just w and the length we can describe it as 4w-6 and the area is w*l=40 and if we multiply them we get the equation 4w%5E2-6w=40
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B-6x%2B-40+=+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=%28-6%29%5E2-4%2A4%2A-40=676.

Discriminant d=676 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+676+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+676+%29%29%2F2%5C4+=+4
x%5B2%5D+=+%28-%28-6%29-sqrt%28+676+%29%29%2F2%5C4+=+-2.5

Quadratic expression 4x%5E2%2B-6x%2B-40 can be factored:
4x%5E2%2B-6x%2B-40+=+4%28x-4%29%2A%28x--2.5%29
Again, the answer is: 4, -2.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-6%2Ax%2B-40+%29

and we take the positive answer of 4 as the width and the lenth is 4(4)-6=10