Question

A square lawn is surrounded by a path 2.5 m wide. If the area of the path is 165 m², find the area of the lawn.​

Answer 1

Answer:

area of lawn is 196 m 2

Step-by-step explanation:

Let length side of lawn =x

area of lawn =x+x=x2

width=2.5m

length increased by 2.5+2.5m=5m

now, area of path including width =(x+5)*(x+5)

given, area of the path 165m2

=(x+5)*(x+5)-x2=165

=x2+10x+25-x2=165

10x+25=165

10x=165-25

10x=140

x=140/10

x=14m

so, the side of the lawn =14m

hence, area of the lawn =14*14=196m2

Answer 2

Answer:

Step-by-step explanation:

Let length side of lawn =x

area of lawn =x+x=x2

width=2.5m

length increased by 2.5+2.5m=5m

now, area of path including width =(x+5)*(x+5)

given, area of the path 165m2

=(x+5)*(x+5)-x2=165

=x2+10x+25-x2=165

10x+25=165

10x=165-25

10x=140

x=140/10

x=14m

so, the side of the lawn =14m

hence, area of the lawn =14*14=196m2