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 lawn.​

Answer 1

Consider the side of the lawn be x

Given width of the path 2.5m

Side of the lawn including path x+2(2.5)=x+5

$\small \bold{Area \: of \: a \: square =(side)^2}$

So, area of lawn = (Area of the lawn including the path) - (Area of the path)

Therefore, According to the given question,:

$\bold{ x^2=(x + 5)^2 −165}$

$\bold{ x^2=(x^2+ 10x +25)−165m^2}$

$\bold{ x^2 =x^2 +10x+25−165}$

$\bold{ x^2 =x^2 +10x−140}$

$\bold{ x^2−140=x^2−10x}$

$\bold{x^2 −x^2−140=−10x}$

−140=−10x

i.e 140=10x

∴x=140/10=14

Since the side of the lawn = 14m

$\small \bold{The \: area \: of \: the \: lawn=(14)^2 \: or \: 196 m^2.}$