SOLUTION: The area of a rectangular tabletop is 6 square feet. If the width is 2 feet shorter than the length, then what are the dimensions?

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Question 286170: The area of a rectangular tabletop is 6 square feet. If the width is 2 feet shorter than the length, then what are the dimensions?
Answer by oberobic(2304)   (Show Source): You can put this solution on YOUR website!
L = length
W = width
A = area = L*W = 6 sq. ft
.
L = W+2
.
Substituting...
.
(W+2)*W = 6
W^2 + 2W = 6
W^2 + 2W -6 =0
.
We cannot factor it, so use the quadratic equation...
.
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=28 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 1.64575131106459, -3.64575131106459. Here's your graph:

.
A negative width is nonsensical, so we'll go with W = approximately 1.6457.
Substituting W=1.6457, we can find L.
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L = W+2 = 1.6457 + 2 = 3.6457
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Checking this solution, is the Area = 6?
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1.6457*3.6457 =5.9997, which within the rounding error caused by using the approximation W = 1.6457.
.
Done.
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