SOLUTION: If the area of the rectangular is 645ft and the length is 12ft larger than the width find its length and its width. please solve in step by step.

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Question 174348: If the area of the rectangular is 645ft and the length is 12ft larger than the width find its length and its width. please solve in step by step.
Answer by nerdybill(7384) (Show Source):
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If the area of the rectangular is 645ft and the length is 12ft larger than the width find its length and its width. please solve in step by step.
.
Let w = width
then
w+12 = length
.
w(w+12) = 645
w^2+12w = 645
w^2+12w-645 = 0
.
Solving via the quadratic equation yields:
w = {20.096, -32.096}
.
Toss out the negative solution we are left with:
width = 20.096 feet
length = 20.096+12 = 32.096 feet
.
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=2724 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 20.0959767013998, -32.0959767013998. Here's your graph: