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

||✪✪ 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 ✰✰ ||

when path is outside the Square , Area of path will be :-

[ ( Length of Square + 2*width of path) * ( breadth of Square + 2*width of path) ] - [ (side of Square)² ] .

Let us assume that, Length breadth of Square is = x m.

So,

→ Area of inner Square = (x * x) = x² m² .

And,

→ Length of outer Square = (x + 2*2.5) = (x + 5)m

→ Breadth of outer Square = (x + 2*2.5) = (x + 5)m

So,

→ Area of Outer Square = (x+5)(x+5) = (x+5)² m² .

Now, Area of Path :- Area of outer Square - Area of inner Square.

putting values we get,

→ (x + 5)² - x² = 165m²

→ (x² + 25 + 10x ) - x² = 165m²

→ 10x + 25 = 165m²

→ 10x = 165 - 25

→ 10x = 140 m²

→ x = (140/10)

→ x = 14m.

So, Area of Square Lawn = (side)² = (14)² = 196m² .

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Answer 2

Given:

Width of the path = 2.5m

Area of path = 165$\sf{m^2}$

To find:

Area of the lawn

Formula Used:

$\sf{Area\:of\:square=(side)^2}$

Identity Used:

$\sf{(a+b)^2=a^2+2ab+b^2}$

Solution:

Let the side of the square lawn be x.

So, area of lawn will be $\sf{x^2}$.

Side of the lawn including the path

$\sf{=x+2.5+2.5=x+5\:metres}$

Area of lawn = Area of lawn including path - Area of path

$\sf{\implies x^2=(x + 5)^2-165}$

$\sf{\implies \cancel{x^2} = \cancel{x^2} +25+10x-165}$

$\sf{\implies 10x=140}$

$\sf{\therefore x = 14 }$

Therefore, side of the lawn is 14 metres.

Area of lawn $\sf{(x^2)}$ = $\sf{14^2}$ = $\sf{196m^2}$

Therefore, area of the lawn is $\bf{196m^2}$.

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