Question

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 1

1) we calculate the area of  the swimmning pool
area of this swimming pool=(22ft)(28 ftt)=616 ft².

2) we calculte the total area of the swimming pool + area of the walkway
Total area=area of the swimming pool + area of the wakway
Total area=616 ft²+336 ft²=952 ft².

3) we can suggest this equation :
x=width
(22+2x)(28+2x)=952
616+44x+56x+4x²=952
4x²+100x-336=0
x²+25x-84=0

x=[-25⁺₋√(625+366)]/2=(-25⁺₋31)/2
we have two solutions:
x₁=(-25-31)/2=-28 this solution is not valid.
x₂=(-25+31)/2=3

Answer: the width of the walkway is 3 ft.