Question

A square lawn is surrounded by a path 2.5m wide. If the area of the path is 165 square metre,dind the area of the lawn

Answer 1

║⊕ANSWER⊕║

Let the side of the lawn be x

Given width of the path = 2.5m

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

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

Area of square=side square

Therefore, we say :

x2 = (x + 5)2 – 165 m2

x2 = (x2 + 10x +25) - 165m2

x2 = x2+ 10x + 25 - 165

x2 = x2 + 10x - 140

x2 - 140 = x2 - 10x

x2 - x2 - 140 = -10x

-140 = -10x

i.e 140 = 10x

Therefore x = 140/10 = 14

Since the side of the lawn = 14 m

The area of the lawn = (14)2 or 196 m2

Answer 2

Given:-

• A square lawn is surrounded by a path 2.5m wide

• Area of the path = 165m²

Have to find:-

What is the area of the lawn ?

Calculations :-

Considering the side of lawn = " x " metre.

Now, According to the Question :-

Given Side of the lawn + measurement of path

= x + 2 × 2.5

= ( x + 5 ). ...... (1)

As we know that,

Using formula of area of square .

Area of square = side²

Firstly find out the side ,

As we know Area of lawn = ( Total area of lawn + the path) - ( Area of the path )

↠ x ² = (x + 5)² - 165

↠ x² = x² + 10x + 25 - 165

↠ x² = x² + 10x - 140

$\longmapsto\tt{ - 10x = - 140}$

$\longmapsto\tt{\cancel\dfrac{- 140}{- 10}=x}$

$\large{\boxed{\bold{x\:=\: 14\:m}}}$

↠ Therefore we got the Side of lawn ↠ 14m

So , we can easily find out the area by using the formula :-

Area = ( Side ) ²

↠ (14)²

↠ 196m²

$\therefore\underline{\boxed{\textsf{A = {\textbf{196m Sq.}}}}} \qquad\qquad \bigg\lgroup\bold{Area \ of \ the \ lawn} \bigg\rgroup$

Additional Information :-

❥ Perimeter of Rectangle = 2( L + B )

❥ Perimeter of square = 4 × Side

❥ Perimeter of triangle = AB + BC + CA

❥ Area of Rectangle = L × B

❥ Area of Square = ( side ) ²

❥ Area of Rhombus = Product of Diagonal/2.

❥ Area of Parallelogram = Base × Height.

❥ Area of triangle = 1/2 × base × height .

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