Question

A rectangular pool has dimensions of 40 feet and 60 feet. 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 what equation could be used to solve the word problem?

Answer 1

Let

x-------> the width of the patio

we understand that

region of the pool=40*60-----> 2400 ft²

vicinity of the patio=[(40+2x)*(60+2x)]-2400

place of the patio=2400 ft²

so

[(40+2x)*(60+2x)]-2400=2400

2400+80x+120x+4x²-4800=0

4x²+200x-2400=0------> divide by 4 both sides----> x²+50x-600=0

therefore

the answer is

x²+50x-600=0

Answer 2

0*60=2,400 ft^2 is the area of the pool.
(40+2x)(60+2x)=2*2,400
2400+120x+80x+4x^2=4,800
4x^2+200x+2,400-4,800=0
4x^2+200x-2,400=0
4(x^2+50x-600)=0
4(x-10)(x+60)=0
x-10=0
x=10 ans. for the width of the patio.
Proof:
(40+2*10)(60+2*10)=2*2,400
(40+20)(60+20)=4,800
60*80=4,800
4,800=4,800