SOLUTION: A rectangular piece of carpet has a length that is 5 yards shorter than twice its width. The area of the carpet is 88 square yards. Find the width only.

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Question 212033: A rectangular piece of carpet has a length that is 5 yards shorter than twice its width. The area of the carpet is 88 square yards. Find the width only.
Answer by drj(1380)   (Show Source): You can put this solution on YOUR website!
A rectangular piece of carpet has a length that is 5 yards shorter than twice its width. The area of the carpet is 88 square yards. Find the width only.

Step 1. Let x be the width of carpet.

Step 2. Let x-5 be the length of carpet

Step 3. Area = width * length






Subtract 88 from both sides of equation to get a quadratic equation



Step 4. This is a quadratic equation. So we can use the formula



where a=1, b=-5 and c=-88.


Now follow the steps below to solve a quadratic equation and select the positive number since we have positive lengths.

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=377 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 12.2082439194738, -7.2082439194738. Here's your graph:




Step 5. So width is 12.21 and length is 7.21 since length = x-5.

Hope this helps! Dr J


For Step-By-Step Videos on Introduction on Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra.


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