Arectangular lawn measuring 8m by 12m is surrounded by apaved path of constant width-w metres.The area of the path is 23m^2. Form aquadratic equation that must be satisfied by width and hence find the width of the path?

Answer 1

with of the whole garden = 8 + 2w
length of the whole garden = 12 + 2w

area of the whole thing = (8+2w)(12+2w)
area of the path = whole thing - area of lawn = 23

(8+2w)(12+2w) - (8)(12) = 23

expand, simplify and solve for w