Question

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a square lawn is surrounded by a path 2.5 m wide .if the area of the path is 165m² find the area of the lawn​

Answer 1

Given:

• Width of path = 2.5 m
• Area of path = 165 m²

To find:

• Area of lawn?

Solution:

Let's consider side of the lawn be x m.

Here, Given that,

• Width of path = 2.5 m

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

We know that,

Area of square = (side)²

So,

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

Here,

• side of lawn = x m
• side of lawn including path = (x + 5) m
• Area of the path = 165 m²

According to the given Question:

⇒ x² = (x + 5)² - 165

⇒ x² = x² + 25 + 10x - 165

⇒ x² = x² + 10x - 140

⇒x² - x² - 10x + 140 = 0

⇒ - 10x + 140 = 0

⇒ - 10x = - 140

⇒ x = 140/10

⇒ x = 14

Therefore,

• The side of square lawn, x = 14 m
• Area of square lawn, x² = (14)² = 196 m²