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) About Me  (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

x%28x-5%29=88

x%5E2-5x=88


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

x%5E2-5x-88=88-88=0

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

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

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 ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-5x%2B-88+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-5%29%5E2-4%2A1%2A-88=377.

Discriminant d=377 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--5%2B-sqrt%28+377+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-5%29%2Bsqrt%28+377+%29%29%2F2%5C1+=+12.2082439194738
x%5B2%5D+=+%28-%28-5%29-sqrt%28+377+%29%29%2F2%5C1+=+-7.2082439194738

Quadratic expression 1x%5E2%2B-5x%2B-88 can be factored:
1x%5E2%2B-5x%2B-88+=+1%28x-12.2082439194738%29%2A%28x--7.2082439194738%29
Again, the answer is: 12.2082439194738, -7.2082439194738. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-5%2Ax%2B-88+%29




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

Hope this helps! Dr J


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