Question

Q. A square lawn is surrounded by a path 2.5m wide. If the area of the path is 165m^2 , find the area of the lawn.


*Please write the whole process of solving

this question.

Answer 1

Answer :

• Area of lawn is 196m²

Given :

• A square lawn is surrounded by a path is 2.5m wide
• Area of path is 165m²

To find :

• Area of the lawn

Solution :

Given ,

• width of path is 2.5m
• Area of path is 165m²

• Let the side of lawn be x
• side of including path = x + 2(2.5) = x + 5m

As we know that,

• Area of square = (side)²

Now we have to find the area of lawn :

• Area of lawn = area of side including path - area of path

⇢ 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

⇢ 140 = 10x

⇢ x = 140/10

⇢ x = 14

side of lawn is 14m

Area of lawn is (14)²m² = 196m²

Hence , Area of lawn is 196m²

Answer 2

Step-by-step explanation:

Area of lawn is 196m²

Given :

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

Area of path is 165m²

To find :

Area of the lawn

Solution :

Given ,

width of path is 2.5m

Area of path is 165m²

Let the side of lawn be x

side of including path = x + 2(2.5) = x + 5m

As we know that,

Area of square = (side)²

Now we have to find the area of lawn :

Area of lawn = area of side including path - area of path

⇢ 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

⇢ 140 = 10x

⇢ x = 140/10

⇢ x = 14

side of lawn is 14m

Area of lawn is (14)²m² = 196m²

Hence , Area of lawn is 196m²