SOLUTION: A rectangular pen for a pet is under construction using 100 feet of fence. A) find the dimensions that give an area of 576 square feet. B) find dimensions that give the max are

Algebra ->  Test -> SOLUTION: A rectangular pen for a pet is under construction using 100 feet of fence. A) find the dimensions that give an area of 576 square feet. B) find dimensions that give the max are      Log On


   

Question 348752: A rectangular pen for a pet is under construction using 100 feet of fence.
A) find the dimensions that give an area of 576 square feet.
B) find dimensions that give the max area.
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
2(x+y)=100 , x+y=50 , x=50-y
xy=576
(50-y)y=576
-y^2+50y=576
y^2-50y+576=0
the answer is: 32, 18 see quadratic solver below.
so y is: 18, 32
so for biggest area would be 25 by 25 =625
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ay%5E2%2Bby%2Bc=0 (in our case 1y%5E2%2B-50y%2B576+=+0) has the following solutons:

y%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=%28-50%29%5E2-4%2A1%2A576=196.

Discriminant d=196 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--50%2B-sqrt%28+196+%29%29%2F2%5Ca.

y%5B1%5D+=+%28-%28-50%29%2Bsqrt%28+196+%29%29%2F2%5C1+=+32
y%5B2%5D+=+%28-%28-50%29-sqrt%28+196+%29%29%2F2%5C1+=+18

Quadratic expression 1y%5E2%2B-50y%2B576 can be factored:
1y%5E2%2B-50y%2B576+=+1%28y-32%29%2A%28y-18%29
Again, the answer is: 32, 18. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-50%2Ax%2B576+%29