SOLUTION: The length of a rectangle is 6 units less than the width. The area of the rectangle is 16 units. What is the length, in units, of the rectangle?

Question 845231: The length of a rectangle is 6 units less than the width. The area of the rectangle is 16 units. What is the length, in units, of the rectangle?

Answer by pmesler(52) (Show Source): You can put this solution on YOUR website!
To start off let's write down the formulas that will be useful. We know that the length L is 6 units less than the width. We can write this
L = W - 6.
Next, let's write the formula for the area of a rectangle.
A = L * W.

Since we know the area we can plug that into the formula. We also know what the length L is. We can plug both of these into the formula.
16 = (W-6) * W
Now we simply solve for W.

16 = W^2-6w
This is starting to look like a quadratic equation. To make it a true quadratic equation, let's bring the 16 to the other side so the equation will equal zero.
W^2-6W - 16 = 0.
Now we simply use the quadratic equation to solve for W.

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=100 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 8, -2. Here's your graph:

The solutions are x = -2 and x = 8. Obviously we can discard -2 as an extraneous root since you can't have a negative length. Therefore the width is 8 units.
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