SOLUTION: The length of a rectangle is 4 inches longer than twice its width. The area of the rectangle is 96 square inches. What is the length and the width of the rectangle?

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Question 607218: The length of a rectangle is 4 inches longer than twice its width. The area of the rectangle is 96 square inches. What is the length and the width of the rectangle?
Answer by asuar010(338)   (Show Source): You can put this solution on YOUR website!
l=2w+4 and the area is 96 so if we set up te equation as l*w=96 and we substitute we obtain 2w^2+4w-96=0
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=784 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 6, -8. Here's your graph:


and we take the positive answer as the solution for w so l=2(6)+4=12+4=16
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