SOLUTION: a rectangle with an area of 112 aquares yards has length 6 yards more than its width. find the perimeter of the rectangle.

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Question 221143: a rectangle with an area of 112 aquares yards has length 6 yards more than its width. find the perimeter of the rectangle.
Answer by drj(1380) About Me  (Show Source):
You can put this solution on YOUR website!
A rectangle with an area of 112 squares yards has length 6 yards more than its width. Find the perimeter of the rectangle.

Step 1. Let w be the width.

Step 2. Let w+6 be the length

Step 3. Perimeter P means adding up all four sides of the rectangle.

Step 4. Then P=w+w+w+6+w+6=4w+12.

Step 5. Area A is the product of the width and length.

Step 6. Then A=w(w+6)=112. or w%5E2%2B6w-112=0

Step 7. Use the quadratic formula to solve for positive. Quadratic formula is given as x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+

where a=1, b=6, and c=-112.

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation aw%5E2%2Bbw%2Bc=0 (in our case 1w%5E2%2B6w%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=%286%29%5E2-4%2A1%2A-112=484.

Discriminant d=484 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+484+%29%29%2F2%5Ca.

w%5B1%5D+=+%28-%286%29%2Bsqrt%28+484+%29%29%2F2%5C1+=+8
w%5B2%5D+=+%28-%286%29-sqrt%28+484+%29%29%2F2%5C1+=+-14

Quadratic expression 1w%5E2%2B6w%2B-112 can be factored:
1w%5E2%2B6w%2B-112+=+1%28w-8%29%2A%28w--14%29
Again, the answer is: 8, -14. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B6%2Ax%2B-112+%29



With w=8 , then in Step 4 P=4w+12=4*8+12=44

Step 8. ANSWER: The perimeter is 44 yards.

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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