A rectangular pool has dimensions of 40 ft. and 60 ft. The pool has a patio area around it that is the same width on all sides.If the patio area equals the area of the pool, how wide is the distance from the pool edge to the patio edge?

If x represents the width of the patio, then which of the following equations could be used to solve the word problem?

x² + 100x + 2,400 = 0
x² - 50x + 600 = 0
x² + 50x - 600 = 0

Question

A rectangular pool has dimensions of 40 ft. and 60 ft. The pool has a patio area around it that is the same width on all sides.If the patio area equals the area of the pool, how wide is the distance from the pool edge to the patio edge?

If x represents the width of the patio, then which of the following equations could be used to solve the word problem?

x² + 100x + 2,400 = 0
x² - 50x + 600 = 0
x² + 50x - 600 = 0

anonymous · Answer

@gerryliyana

anonymous · Answer

wait

anonymous · Answer

based on the text

area of pool = area of patio

anonymous · Answer

and we've known that the are of the pool = 40 ft x 60 ft =  2400 ft^2

anonymous · Answer

because the area of pool = area of patio = 2400, we are allowed to write

The area of the pool plus the patio = 2(2400) = 4800

anonymous · Answer

Okay..?

anonymous · Answer

The area of the pool plus the patio can also be written in (2x+40)*(2x+60), 
so 
(2x+40)*(2x+60)=4800
4x^2 + 120x + 80x + 2400 = 4800
4x^2 + 200x + 2400 = 4800

dividing both sides of the equation by 4 yields

x^2 + 50x + 600 = 1200
x^2 + 50x + 600 - 1200 = 0
x^2 + 50x - 600 = 0

anonymous · Answer

@xo_kansasprincess_xo : got it?

anonymous · Answer

x² + 50x - 600 = 0 is the answer

anonymous · Answer

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anonymous · Answer

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