SOLUTION: A rectangle has a length that is 5 feet more than its width. The area of this rectangle is 84 square feet. What is the width and length of this rectangle?

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Question 613635: A rectangle has a length that is 5 feet more than its width. The area of this rectangle is 84 square feet. What is the width and length of this rectangle?
Answer by radh(108) (Show Source):
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We know that to find the area of a rectangle, you use this formula: . Let's convert the words into something mathematical.

A rectangle has a length that is 5 feet more than it's width (w+5). The area of this rectangle is 84 square feet (=84).

Let's plug in what we know into the area formula. .
Simplify: to . Let's use the quadratic formula to simplify.

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

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=361 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 7, -12. Here's your graph:

The area can't be negative, so we're assuming . That means that the width of the rectangle is 7, and the length . The length is 12.