Question

a square lawn has a 2 metre wide path surrounding if it area of the path is 136 square find the area of the lawn​

Answer 1

Answer:

Let ABCD be the square lawn and PQRS be the outer boundary of the square path.

Let the side of the lawn AB be x m

area of the square lawn = x²

length PQ = ( X + 2+ 2) = ( X + 4 ) M

area of PQRS = ( X+ 4)²= ( X² + 8X + 16) M²

area of the path = area of PQRS - area of the square lawn.

136 = x²+ 8x+ 16-x²

136= 8x+16

136-16=8x

120÷8= x

x=15

side of the lawn = 15m

area of the lawn = (side)²

= (15)²

= 225 m²