SOLUTION: a 20-ft by 40-ft rectangular swimming pool is surrounded by a walkway of uniform width. if the total are of walkway is 544 ft^2, how wide is the walkway

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Question 836685: a 20-ft by 40-ft rectangular swimming pool is surrounded by a walkway of uniform width. if the total are of walkway is 544 ft^2, how wide is the walkway
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Two-D pool area not including walls, 20%2A40%2Aft%5E2.
The pool area AND the walkway combined area, %2820%2B2w%29%2840%2B2w%29 and we do not yet know the value. The unknown variable w is the walkway width.

We can say THIS:
%2820%2B2w%29%2840%2B2w%29-20%2A40=544; this must be understood before continuing.

READY?

4%2810%2Bw%29%2820%2Bw%29-4%2A5%2A40=544
%2810%2Bw%29%2820%2Bw%29-5%2A40=136
200%2B30w%2Bw%5E2-200-136=0
highlight_green%28w%5E2%2B30w-136=0%29
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136=34*4, factoring is a good method for the quadratic.
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%28w-4%29%28w%2B34%29=0
The only sensible solution is highlight%28w=4%29 feet.