SOLUTION: designing a pool where the area 16 and the perimeter is 20.

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Question 413587: designing a pool where the area 16 and the perimeter is 20.
Answer by nerdybill(7384)   (Show Source): You can put this solution on YOUR website!
designing a pool where the area 16 and the perimeter is 20.
.
assuming it's a rectangular pool...
.
Let W = width
and L = length
.
from knowledge of perimeter:
2(W+L) = 20
W+L = 10 (equation 1)
.
from knowledge of area:
WL = 16 (equation 2)
.
Solving equation 1 for L we get:
L = 10-W
Substitute into equation 2:
W(10-W) = 16
W^2+10W = 16
W^2+10W-16 = 0
Applying the quadratic formula we get:
W = {1.4, -11.4}
.
Find L by substitutiting above into equation 1:
1.4+L = 10
L = 8.6
.
Dimensions are: 1.4 by 8.6
.
Details of quadratic follows
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=164 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 1.40312423743285, -11.4031242374328. Here's your graph:
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