SOLUTION: A rectangular storage area is 8.0 meter longer than it is wide. If the area is 28m^2, what are its dimensions?

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Question 437160: A rectangular storage area is 8.0 meter longer than it is wide. If the area is 28m^2, what are its dimensions?
Answer by oberobic(2304)   (Show Source): You can put this solution on YOUR website!
Area = Length * Width
A = L*W
.
We're told
A = 28
.
We're also told the length is 8 meters greater than width.
L = W+8
.
L * W = A
.
Substituting:
(W+8) * W = 28
W^2 + 8W = 28
Subtract 28 from both sides
W^2 + 8W - 28 = 0
.
This does not factor easily, 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=176 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 2.6332495807108, -10.6332495807108. Here's your graph:

.
A negative value for W does not make sense, so we choose W = 2.633.
L = W + 8 = 10.633.
.
Checking.
10.633*2.633=27.9966 or about 28.
.
Done.
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