Question

A square lawn has a 3 m wide path surrounding it.

If the area of the path is 156 m2, find the area of the lawn.

Let’s assume the side length of the lawn to be l. Then the side length of the ‘outer’ square equals
.

Answer 1

Answer:

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

Let side of the lawn AB be x m.

Area of the square lawn = x^2

Given that Length PQ = (x + 3 + 3) = (x + 6) m

Area of PQRS = (x + 6)^2 = (x^2 + 12x + 36) m^2

Now, Area of the path = Area of PQRS – Area of the square lawn.

156 = (x^2 + 12x + 36) - x^2

156 = 12x + 36

156 - 36 = 12x

120 = 12x

x = 10m

Side of the lawn = 10m

Hence, Area of the lawn = (Side)2 

= (10)^2

= 100m^2

Answer 2

Answer:

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

Let side of the lawn AB be x m.

Area of the square lawn = x^2

Given that Length PQ = (x + 3 + 3) = (x + 6) m

Area of PQRS = (x + 6)^2 = (x^2 + 12x + 36) m^2

Now, Area of the path = Area of PQRS – Area of the square lawn.

156 = (x^2 + 12x + 36) - x^2

156 = 12x + 36

156 - 36 = 12x

120 = 12x

x = 10m

Side of the lawn = 10m

Hence, Area of the lawn = (Side)2  

= (10)^2