Question

A square lawn is surrounded by a path 2. 5 m wide. If the area of the path is165 square metre find the area of the lawn.

Answer 1

Given :-

• Area of the path = 165 m²

• Width of the path = 2.5 m

To Find:-

• Area of the lawn = ?

Solution:-

Let the side of the square lawn be S m.

Outer side of lawn = S + 2.5 + 2.5

Outer side of lawn = ( S + 5 ) m

Area of the path = ( S + 5 )² - S²

A/Q,

$\bf\implies$ S² + 10s + 25 - S² = 165

$\bf\implies$10s = 165 - 25

$\bf\implies$10s = 140

$\bf\implies$S = 140/10

$\bf\implies$S = 14 m

Area of lawn = (a)²

Area of lawn = (14)²

Area of lawn = 196 m²

Hence , Area of lawn is 196 m²

Formula :-

• Area of Square = (Side)² = (a)²

• perimeter of Square = 4 × Side = 4a

Answer 2

$\huge\underline\mathrm\blue{GIVEN:-}$

• Width of the path around a square lawn = 2.5m
• Area of Path = 165 m²

$\huge\underline\mathrm\blue{TO\:FIND:-}$

Find the area of the square lawn = ?

$\huge\underline\mathrm\blue{SOLUTION:-}$

【We have given that, A square lawn is surrounded by a path 2. 5 m wide】

☞Firstly, need to find the side of the square lawn

❛Let the side of the square lawn be 'x' m❜ 

According to question :-

Outer side of the square lawn = （2 $\times$ width of path + x ）

$\longmapsto$$\rm{( 2.5 + 2.5 + x)}$

$\longmapsto$$\rm{( 5 + x)}$

$\longmapsto$ $\rm{Area \:of \:path=(5+x)^2-x^2= 165}$

$\longmapsto$ $\rm{x^2 + 10x + 25 -x^2=165}$[∴ By Identity (a+b)² = a² + b² + 2ab ]

$\longmapsto$ $\rm{\cancel{x^2} + 10x + 25 -\cancel{x^2}=165}$

$\longmapsto$ $\rm{ 10x + 25 = 165}$

$\longmapsto$ $\rm{ 10x = 165 - 25}$

$\longmapsto$ $\rm{ 10x = 140}$

$\longmapsto$ $\rm{ x = \cancel\dfrac{140}{10}}$

$\longmapsto$ $\Large\rm\red{ x = 14\: m}$

★Now, we have to find the area of the square lawn

To find the area of the square lawn, we use the formula of area of square:-

$\large{\boxed{\bf{\red{Area \: of \: square = (a)^2}}}}$

☞On putting the values in the formula, we get

$\rightharpoonup$$\rm{Area = (14)^2}$

$\rightharpoonup$$\rm{Area = 196\: m^2}$

Thus, the area of the square lawn is 196 m²

$\Large\underline\mathrm\blue{FINAL\:ANSWER:-}$

$\Large{\boxed{\boxed{\bf{\red{Area \: of \: square\: Lawn= 196\: m^2}}}}}$