SOLUTION: a dog pen has an area of 60 square feet the width of the pendants two feet shorter than the left find the length of the pen?

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: a dog pen has an area of 60 square feet the width of the pendants two feet shorter than the left find the length of the pen?      Log On


   

Question 1071205: a dog pen has an area of 60 square feet the width of the pendants two feet shorter than the left find the length of the pen?
Answer by Dirichlet(3) About Me  (Show Source):
You can put this solution on YOUR website!
Let:
w = the width of the pen
l = the length of the pen
The width is 2 feet shorter than the width, so this gives:
w+=+l+-+2
The area A of a rectangle is:
A+=+l%2Aw
Substituting in w, we get:
A+=+%28l-2%29%2Al
The area A also equals 60. So, we get:

60+=+%28l-2%29%2Al
Distribute l:
60+=+l%5E2+-+2l
Bring the 60 over and we get:
+0+=+l%5E2+-+2l+-+60
Using the quadratic formula,
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-2x%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=%28-2%29%5E2-4%2A1%2A-60=244.

Discriminant d=244 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--2%2B-sqrt%28+244+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-2%29%2Bsqrt%28+244+%29%29%2F2%5C1+=+8.81024967590665
x%5B2%5D+=+%28-%28-2%29-sqrt%28+244+%29%29%2F2%5C1+=+-6.81024967590665

Quadratic expression 1x%5E2%2B-2x%2B-60 can be factored:
1x%5E2%2B-2x%2B-60+=+%28x-8.81024967590665%29%2A%28x--6.81024967590665%29
Again, the answer is: 8.81024967590665, -6.81024967590665. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-2%2Ax%2B-60+%29


(Note: l is and ugly number!)
Only the positive answer makes sense, 8.8102...
To find w, subtract 2 from l.