+318 A pool measuring 18 meters by 22 meters is surrounded by a path of uniform width. If the area of the pool and the path combined is 896 square meters, what is the width of the path?
+129852 Let the width of the path = W
So we have that
(18 + 2W) ( 22 + 2W) = 896 simplfy
396 + 44W + 36W + 4W^2 = 896
4W^2 + 80W + 396 = 896 subtract 896 from both sides
4W^2 + 80W - 500 = 0 divide through by 4
W^2 + 20W - 125 = 0 factor as
(W - 5) ( W + 25) = 0
Setting each factor to 0 and solving for W produces W = 5 or W = -25
Obviously....only the positive answer makes sense....so...
The width of the path = 5 ft
