SOLUTION: The rectangular tabletop has a width that is two feet less than four times its length. If the area of the tabletop is 20ft^2, what are the dimensions of the tabletop?

Question 62270: The rectangular tabletop has a width that is two feet less than four times its length. If the area of the tabletop is 20ft^2, what are the dimensions of the tabletop?
Answer by tutorcecilia(2152) (Show Source): You can put this solution on YOUR website!
Area = (length)(width) [use the formula for the area of a rectangle]
Area = 20 ft^2
Length=L
Width=4L-2
.
20=(L)(4L-2)[plug-in the values]
20=4L^2-2L [simplify]
0=4L^2-2L-20 [set the equation equal to zero and factor using the quadratic equation]
.
L=2.5[use this answer since it is a positive measurement]
L=-2.00 [eliminate this answer since measurements cannot be negative]
.
Length = 2.5
Width = 4L-2=(4)(2.5)-2=8
.
Check by plugging all of the values back into the formula for the area of a rectangle:
Area = (2.5)(8)
A=20 [checks out]
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