Hot tubs are in ground swimming pools are some times surrounded by border of tiles. The square hot tub has a side of length s feet. The tub is surrounded y a border tiles. Each square tiles measure 1 ft.to find the tile you have to use this: 4(s+1) now how is that expression same to (s+2)^2-s^2
(s+2)? - s? = (s? + 4s + 4) - s? = 4s + 4 = 4(s+1).
(s+2)^2-s^2 would provide the area of the tile border. It is equivalent to the area of the whole hot tub installation, including tile, minus the area of the tub itself. 4(s+1) would be a length in feet, and is not equivalent to any area. The perimeter of the hot tub is 4s, and the perimeter of the whole installation, including the tile is 4(s+2). 4(s+1), ignoring units, would give the number of tiles required for the border, which if multiplied by the area of one tile (1 ft^2) would give the area of the tile border. (s+2)^2-s^2 = s^2 + 4s + 4 - s^2 = 4s + 4 = = 4(s + 1) sq. ft. is also the area of the tile border. So they are the same, if you account for the difference in units.
