SOLUTION: The length of a rectangle is 5 centemeters less than three times its width. Its area is 12 square centemeters. Find the dimentions of the rectangle.

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Question 692287: The length of a rectangle is 5 centemeters less than three times its width. Its area is 12 square centemeters. Find the dimentions of the rectangle.
Answer by Stitch(470) (Show Source):
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Set-Up
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A = L * W (Area of a rectangle)
Given: A = 12, L = 3W - 5
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Solution:
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Substitute the given information into the equation for the area of a rectangle
Simplify
Subtract 12 from both sides

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=169 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 3, -1.33333333333333. Here's your graph:

The answers were W = 3cm or -1.333cm. But since you can not have a negative width. Just use the 3cm
Now we can find the length
L = 3W - 5
Plug 3 in for W