SOLUTION: jess and her husband made a rectangular swimming pool measuring 28 feet by 42 feet. They want to add a decorative tile border of uniform width around sides of the pool. How wide ca

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Question 1008424: jess and her husband made a rectangular swimming pool measuring 28 feet by 42 feet. They want to add a decorative tile border of uniform width around sides of the pool. How wide can they make the tile border if they purchased enough tile to cover 624 square feet?
The maximum width of the border can be [ ] feet?
(Type an exact answer using radicals as needed)
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!

With length in ft and areas in square feet,
system%28pool_area=42%2A28%2Ctotal_area=%2842%2B2w%29%2A%2828%2B2w%29%2Cborder_area=624%29-->%2842%2B2w%29%2A%2828%2B2w%29-42%2A28=624-->42%2A28%2B42%2A%282w%29%2B%282w%29%2A28%2B%282w%29%2A%282w%29-42%2A28=624-->42%2A28%2B84w%2B56w%2B4w%5E2-42%2A28=624-->140w%2B4w%5E2=624-->35w%2Bw%5E2=156
We can solve the quadratic equation 35w%2Bw%5E2=156 by any method
("completing the square", factoring, or using the quadratic formula),
to get the solutions
w=4 and w=-36 .
For this word problem, the solution w=-36 does not make sense,
so the maximum with for the border (achieved using all the tile available) is highlight%284ft%29 .

SOLVING THE EQUATION BY COMPLETING THE SQUARE:
w%5E2%2B35w=156
w%5E2%2B35w%2B%2835%2F2%29%5E2-%2835%2F2%29%5E2=156
%28w%2B35%2F2%29%5E2-1225%2F4=156
%28w%2B35%2F2%29%5E2=1225%2F4%2B156
%28w%2B35%2F2%29%5E2=1225%2F4%2B624%2F4
%28w%2B35%2F2%29%5E2=1849%2F4
%28w%2B35%2F2%29%5E2=%2843%2F2%29%5E2-->system%28w%2B35%2F2=43%2F2%2C%22or%22%2Cw%2B35%2F2=-43%2F2%29-->system%28w=43%2F2-35%2F2%2C%22or%22%2Cw=-43%2F2-35%2F2%29-->system%28w=8%2F2%2C%22or%22%2Cw=-78%2F2%29-->system%28w=4%2C%22or%22%2Cw=-36%29