Question

A square lawn has a 2m wide path surrounding it. If the area of the path is 136 square m, find the area of the lawn.Please give the ans with detailed steps.​

Answer 1

Answer:the area of the square lawn = side square=(15m)^2
=225m^2

Step-by-step explanation:
let ABCD be the square lawn and PQRS be outer boundary of the square path 136 area
let side of the lawn AB be x m.
area of the square = side square
So area of square lawn with side AB=x^2
Given length of PQ=(x+2+2)=(x+4)m
Area of PQRS=(x+4)^2=(x^2+8x+16)
Now, area of the path =area of PQRS-Area of square lawn
136=x^2+8x+16-x^2
136=8x+16
136-16=8x
120=8x
x=120/8
x=15
The side of the square lawn=15m
Hence the area of the square lawn = side square=(15m)^2
=225m^2