SOLUTION: The area of a table top is 52 square feet, and twice the length is 3 feet shorter than two times the width. Find the perimeter of the table top. I always do just fine working th

Algebra ->  Rectangles -> SOLUTION: The area of a table top is 52 square feet, and twice the length is 3 feet shorter than two times the width. Find the perimeter of the table top. I always do just fine working th      Log On


   

Question 997948: The area of a table top is 52 square feet, and twice the length is 3 feet shorter than two times the width. Find the perimeter of the table top.
I always do just fine working the problem out until I have to apply the zero product rule. I see examples where the two numbers used have the product to equal 'c' but they do not add to equal 'b' in the equation and it is frustrating to me to understand this when that was what I was told to do.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
The area of a table top is 52 square feet, and twice the length is 3 feet shorter than two times the width. Find the perimeter of the table top.

let length be l
width be w
2l=2w-3
l+=+%282w-3%29%2F2+

l * w = 52
substitute l
%28%282w-3%29%2F2%29+%2A+w+=52

multiply equation by 2
(2w-3 )*w = 52*2
2w%5E2-3w+=104
2w%5E2-3w-104=0

2w%5E2-16w%2B13w-104=0
2w(w-8)+13(w-8)=0
(2w+13)(w-8)=0
If 2w+13 =0
then w = -7.5
not applicable
if w-8=0
the dimensions are 8 and 6.5 feet
w= 8