SOLUTION: 2. The perimeter of a rectangular flower garden is 60 m and its area is 225 m2. Find the length of the garden.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: 2. The perimeter of a rectangular flower garden is 60 m and its area is 225 m2. Find the length of the garden.      Log On


   

Question 971060: 2. The perimeter of a rectangular flower garden is 60 m and its area is 225 m2. Find the length of the garden.
Answer by amarjeeth123(569) About Me  (Show Source):
You can put this solution on YOUR website!
Let the length of the garden be x.
Perimeter=2(length+width)
2(x+width)=60
x+width=30
width=30-x
Area of the garden=225
Area=length*width
x(30-x)=225
30x-x^2=225
x^2-30x+225=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-30x%2B225+=+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=%28-30%29%5E2-4%2A1%2A225=0.

Discriminant d=0 is zero! That means that there is only one solution: x+=+%28-%28-30%29%29%2F2%5C1.
Expression can be factored: 1x%5E2%2B-30x%2B225+=+1%28x-15%29%2A%28x-15%29

Again, the answer is: 15, 15. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-30%2Ax%2B225+%29

x=15
The length of the garden is 15 m.