Let the side of the lawn = am
Then side of big square = (a + 2(2)) m
= (a + 4)m
Area of the path – Area of large square – Area of smaller square
136 = (a + 4)2 – a2
136 = a2 + (2 x a x 4) + 42 – a2
136 = a2 + 8a + 16 – a2
136 = 8a + 16
136 = 8(a + 2)
Dividing by 8
17 = a + 2
Subtracting 2 on both sides
17 – 3 = a + 2 – 2
15 = a
∴ Side of small square = 15 m
Area of square = (side x side) sq. units
∴ Area of the lawn = (15 x 15)m = 225 m
∴ Area of the lawn = 225 m2