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) About Me  (Show Source):
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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 ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-5x%2B-88+=+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=%28-5%29%5E2-4%2A2%2A-88=729.

Discriminant d=729 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+729+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+729+%29%29%2F2%5C2+=+8
x%5B2%5D+=+%28-%28-5%29-sqrt%28+729+%29%29%2F2%5C2+=+-5.5

Quadratic expression 2x%5E2%2B-5x%2B-88 can be factored:
2x%5E2%2B-5x%2B-88+=+2%28x-8%29%2A%28x--5.5%29
Again, the answer is: 8, -5.5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-5%2Ax%2B-88+%29


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