POTW #1 Answer and Explanation

Since the POTW is closed, I decided to give the answer now because anyone else that finishes the problem will not deserve any credit, only the first five do (This time, first six because Tyler E. was an exception). I know it has only been about 3 days, but so what?



The perimeter of the rectangle would be 56 inches. The length was 16 inches and the width was 12 inches. There were many ways to do this, but the easiest would be to use algebra. However, you would have to know how to simplify quadratic equations, which average eighth graders wouldn't know. Here's a step-by-step process of solving this question the algebraic way.

First, you would get the equation:
x(x+4)=192 where x stands for the width

Distribute the x:
x^2+4x=192

Make the equation equal 0:
x^2+4x-192=0

Simplify the quadratic equation: (Note: if you do not know how to do this, then you couldn't have solved this question the algebraic way)
(x-12)(x+16)=0

Solve for x: (Note: There are usually two answers for a quadratic equation)
x=12 or -16

Use your logic, the width couldn't be a negative number, so the width would be 12.
Now, if the width was 12, the the length would be four more, or 16. Thus the perimeter would be 12+12+16+16=56

(Note: please be sure to find out what the question is asking for. A few people gave me 12 and 16, which were the dimensions of the rectangle. However, the problem asked for the perimeter. I did not take off for this error because this was the first POTW (Tyler E. is an exception). I will take off 2 points in the future though.)


Any questions or comments? Post a comment or email me at twang7888@yahoo.com.