SOLUTION: Fred's retangular dog pen must have an area of 400 square feet. Also the length must be 12 feet longer then the width. Find the dimensions of the pen. The width of the pen is

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: Fred's retangular dog pen must have an area of 400 square feet. Also the length must be 12 feet longer then the width. Find the dimensions of the pen. The width of the pen is       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 436858: Fred's retangular dog pen must have an area of 400 square feet. Also the length must be 12 feet longer then the width. Find the dimensions of the pen.
The width of the pen is
The length of the pen is
(Simplify your answer. Type a exact answer, using radicls as needed)
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
Area=LxW
(x+12)x=400
x2+12x-400=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B12x%2B-400+=+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=%2812%29%5E2-4%2A1%2A-400=1744.

Discriminant d=1744 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-12%2B-sqrt%28+1744+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2812%29%2Bsqrt%28+1744+%29%29%2F2%5C1+=+14.8806130178211
x%5B2%5D+=+%28-%2812%29-sqrt%28+1744+%29%29%2F2%5C1+=+-26.8806130178211

Quadratic expression 1x%5E2%2B12x%2B-400 can be factored:
1x%5E2%2B12x%2B-400+=+1%28x-14.8806130178211%29%2A%28x--26.8806130178211%29
Again, the answer is: 14.8806130178211, -26.8806130178211. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B12%2Ax%2B-400+%29

Throwing out the negative answer, we get width=14.88, and length to be 26.88.