SOLUTION: The length of a rectangle is 9 inches more than the width. Its area is 112 square inches. Find the dimensions of the rectangle.

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Question 227095: The length of a rectangle is 9 inches more than the width. Its area is 112 square inches. Find the dimensions of the rectangle.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
The length of a rectangle is 9 inches more than the width. Its area is 112 square inches. Find the dimensions of the rectangle.

Step 1. The area A of a rectangle is given as A=length*width.

Step 2. Let w be the width.

Step 3. Let w+9 be the length

Step 4. Then, A=w(w+9)=112 or w^2+9w-112=0

Step 5. To solve, use the quadratic formula given as

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

where a=1, b=9, and c=-112

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aw%5E2%2Bbw%2Bc=0 (in our case 1w%5E2%2B9w%2B-112+=+0) has the following solutons:

w%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=%289%29%5E2-4%2A1%2A-112=529.

Discriminant d=529 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-9%2B-sqrt%28+529+%29%29%2F2%5Ca.

w%5B1%5D+=+%28-%289%29%2Bsqrt%28+529+%29%29%2F2%5C1+=+7
w%5B2%5D+=+%28-%289%29-sqrt%28+529+%29%29%2F2%5C1+=+-16

Quadratic expression 1w%5E2%2B9w%2B-112 can be factored:
1w%5E2%2B9w%2B-112+=+1%28w-7%29%2A%28w--16%29
Again, the answer is: 7, -16. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B9%2Ax%2B-112+%29



For w=7 , then w+9=16 and A=7*16=112 which is a true statement.

Step 6. ANSWER: The width is 7 inches and the length is 9 inches.

I hope the above steps were helpful.

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

And good luck in your studies!

Respectfully,
Dr J

drjctu@gmail.com

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