SOLUTION: The area is 44 square feet, and twice the length is 5 feet shorter than two times the width. What is the perimeter?

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Question 526076: The area is 44 square feet, and twice the length is 5 feet shorter than two times the width. What is the perimeter?
Answer by Maths68(1474)   (Show Source): You can put this solution on YOUR website!
The area is 44 square feet, and twice the length is 5 feet shorter than two times the width. What is the perimeter?
Area = A = 4 ft^2
Length = 2l = (2w-5)ft
Length = l = (2w-5)/2 ft
Length = ?
Width = ?
Length * Width = Area of Rectangle
l*w=A
((2w-5)/2)*(w) = 44
(2w^2-5w)/2 = 44
(2w^2-5w) = 44*2
2w^2-5w = 88
2w^2-5w-88=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=729 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 8, -5.5. Here's your graph:


w=-5.5 not possible
w=8


Length = 2l = (2w-5)ft
Length = l = (2w-5)/2 = (2(8)-5)/2=(16-5)/2=11/2=5.5ft

Length = 5.5 ft
Width = 8 ft
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