Question

harold goldstein and his wife elaine recently installed a built in rectangular swimming pool measuring 13 ft by 27 ft. they want to add a decorative tile border of uniform width around all sides of the pool. how wide can they make the tile border if they purchased enough tile to cover 176 sq feet? the max width of the border can be ? ft? HELP!! need solution, very confused :(

Answer 1

Let 0 < W be the width of the tile border in feet and A = 296 be the area of this border in square feet. Then we may state:

\[(28+2W)(42+2W)-28\times42 = 296\]
Divide through by 4:
\[(14+W)(21+W)-14\times21=74\]
\[W ^{2}+35W-74=0\]
Factor:
\[(W-2)(W+37)=0\]
Taking the positive root, we find:
\[W=2\]

Answer 2

thank you so much

Answer 3

No problem!