A square lawn is surrounded by a path 2.5m wide, if the area of the path is 165m square, find the area of the lawn

Answer 1

let x be the length of each of the lawn's side, and y be the length of each of the whole land's side (including the path surrounding the lawn)

y^2 - x^2 = 165
y = x + 5
substitute y:
(x+5)^2 - x^2 = 165
hence: x^2 + 10x + 25 - x^2 = 165
10x = 140
x = 14
area of lawn: 14^2

Answer 2

196