Question

a square lawn is surrounded by a path 2.5m wide. if the area of the path is 165m,find the area of the lawn.

Answer 1

Answer:

196 m²

Step-by-step explanation:

Let the side of lawn be x.

Given that,

Width of the path = 2.5 m

Side of lawn including path = x + 2 * 2.5

                                              = (x + 5) m

∴ Area of lawn = (Area of lawn including path) - (Area of path)

We know that ;

Area of square = (side)²

⇒ x² = (x + 5)² - 165 m²

⇒ x² = x² + 5² + 2 * x * 5 - 165

⇒ x² = x² + 25 + 10x - 165

⇒ x² = x² + 10x - 140

⇒ x² - 10x = x² - 140

⇒ x² - x² - 10x = - 140

⇒ - 10x = - 140

⇒ 10x = 140

⇒ x = $\frac{140}{10}$

⇒ x = 14 m

Side of lawn = 14 m

So, Area of lawn = (side)²

                            = (14)²

                            = 196 m²

Hence, the area of lawn is 196 m².

Answer 2

Solution :

Assuming the Side be 'y'

We know that ,

Area of square = ( Side × Side )

➨ y × y

Now , given -  

Width = 2.5 m

So , now Length increases by 5m

Then

Area including width :-

➨ (y+5) × (y+5)

Hence ,

According to the Query :-

➨ [(y+5) × (y+5)]-(y × y) = 165

➨ y² + 10y + 25 - y² = 165

➨ 10y + 25 = 165

➨ 10y = 165 - 25

➨ 10y = 140

➨ y = 140/10 = 14

➨ y = 14

Hence , 14 m is side of the lawn.

Then ,

Area of the lawn :-

➨ y × y = 14 × 14

➨ 196 m²