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

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) (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

Step 7. Use the quadratic formula to solve for positive. Quadratic formula is given as

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

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=484 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 8, -14. Here's your graph:

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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