Question

a square lawn is surrounded by 6m wide path around it . if the area of the path is 360 square metre . find the area of lawn.​

Answer 1

Step-by-step explanation:

Consider the side of the lawn be x

Given width of the path = 3m

Side of the lawn including path = x + 2(3m) = x + 6m

So, area of lawn =

(Area of the lawn including the path) - (Area of the path)

Area of a square = (side)*2

Therefore, we say :

x*2 = (x + 6)2 – 180m2

x*2 = (x*2 + 12x +36) - 180m2

x*2 = x*2+ 12x + 36 - 180

x*2 = x*2 + 12x - 144

x*2 - 144 = x*2 - 12x

x*2 - x2 - 144 = -12x

-144 = -12x

i.e 144 = 12x

Hope it will help you .

Answer 2

${\blue{\underline{\underline{\purple{\textsf{\textbf{Answer : }}}}}}}$

➙ Area of the square lawn is 81m²

${\blue{\underline{\underline{\purple{\textsf{\textbf{Step-by-step explanation: }}}}}}}$

Step 1 : Find the area of ABCD :

Let's assume the each side of the square lawn $x$ metres.

Area of the square ABCD :

$\to (x)^2$

$\to x^2$ metres².

Step 2 : Find the area of PQRS :

Here, the each side of PQRS will be :

$\to (x + 12)$ metres.

Area of PQRS :

$\to (x + 12)^2$ m²

$\to x^2 + 24x + 144$ m²

Step 3 : Find the each side of the square lawn :

We know that,

Area of the path :

→ Area of PQRS - Area of ABCD.

But, area of the path is 360m² (given)

So, we can say that,

$\implies ( {x}^{2} + 24x + 144) - {x}^{2} = 360$

Solving for $x$ :

$\implies {x}^{2} + 24x + 144 - {x}^{2} = 360$

$\implies 24x + 144 = 360$

$\implies \: 24x = 360 - 144$

$\implies 24x = 216$

$\implies x = \frac{216}{24}$

$\implies x = {\bf{\blue{ 9 }}}$

∴The each side of the square lawn is 9cm.

Area of the lawn will be :

→ (9m)²

→ 81m²

Area of the lawn is 81m²