SOLUTION: Suppose the width of a rectangle is 5cm less than half its length. Its area is 72 cm squared. What is the length and width of the rectangle?

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Question 330594: Suppose the width of a rectangle is 5cm less than half its length. Its area is 72 cm squared. What is the length and width of the rectangle?
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
a=lw know your formulas
a=72
w=(l/2)-5
72=l%28%28l%2F2%29-5%29
72=%28l%5E2%2F2%29-5l
144=l%5E2-10l
0=l%5E2-10l-144 view below for quadratic explaination
l=18
72/18=w
w=4
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation al%5E2%2Bbl%2Bc=0 (in our case 1l%5E2%2B-10l%2B-144+=+0) has the following solutons:

l%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=%28-10%29%5E2-4%2A1%2A-144=676.

Discriminant d=676 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--10%2B-sqrt%28+676+%29%29%2F2%5Ca.

l%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+676+%29%29%2F2%5C1+=+18
l%5B2%5D+=+%28-%28-10%29-sqrt%28+676+%29%29%2F2%5C1+=+-8

Quadratic expression 1l%5E2%2B-10l%2B-144 can be factored:
1l%5E2%2B-10l%2B-144+=+1%28l-18%29%2A%28l--8%29
Again, the answer is: 18, -8. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-10%2Ax%2B-144+%29