A rectangular swimming pool that is 10 ft wide by 16 ft long is surrounded by a cement sidewalk of uniform width. If the area of the sidewalk is 155 ft2, what is its width?

Hello,

Let 's x the width of the sidewalk.

Area of the swimming pool = 10*16=160 (ft²)

Area of the sideway+the swimming pool = (16+2x) * (10+2x) = 160+155

==>160+20x+32x+4x²=160+155

==>4x²+52x-155=0

Δ=52²+4*4*155=5184=72²

==>x = (-52+72) / 2=5/2 or x=a negative to exclude.

Width of the sideway=5/2 ft