SOLUTION: a 22-ft by 28-ft rectangular swimming pool is surrounded by a walkway of uniform width. if the total area of the walkway is 336 ft2, how wide is the walkway?

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Question 897671: a 22-ft by 28-ft rectangular swimming pool is surrounded by a walkway of uniform width. if the total area of the walkway is 336 ft2, how wide is the walkway?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
I will setup the majority of the solution process completely in symbols, and you can finish from where my response stops.

Say your variables are this way:
w = 22 feet pool width
L = 28 feet pool length
A = area of just the walkway around pool
x = unknown uniform width of the walkway around pool

The unknown variable to solve in this arrangement is x.

Pool area, wL.
Total area of pool and walkway, %28w%2B2x%29%28L%2B2x%29
WALKWAY AREA, highlight_green%28%28w%2B2x%29%28L%2B2x%29-wL=A%29

Solve for x, the uniform width of walkway.
wL%2B2Lx%2B2wx%2B4x%5E2-wL=A
4x%5E2%2B12Lx%2B2wx=A
4x%5E2%2B%282w%2B2L%29x-A=0
You could choose to substitute values now and perform some numeric simplification, often possible in academic problems; but you do not always know.

Staying in symbolism,
x=%28-2w-2L%2B-+sqrt%284%28w%2BL%29%5E2-4%2A4%2A%28-A%29%29%29%2F%282%2A4%29
x=%28-2w-2L%2B-+sqrt%284%28w%2BL%29%5E2%2B16A%29%29%2F%282%2A4%29
x=%28-2w-2L%2B-+2sqrt%28%28w%2BL%29%5E2%2B4A%29%29%2F%282%2A4%29
highlight%28x=%28-w-L%2B-+sqrt%28%28w%2BL%29%5E2%2B4A%29%29%2F4%29
One of these will make sense and one of them will not make sense. Choose the one with sensible meaning.