Question

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

Answer 1

Answer:

Step-by-step explanation:

Consider 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 a square = (side)²

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

Answer:

Given:-

⇢ A square lawn is surrounded by a path of 2.5m wide. If the area of path is 165m².

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Find:-

⇢ Find the area of the lawn.

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Using forumula:-

We know that,

★ Area of square = Side² ★

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Calculations:-

⇢ (x + 5)² - 165²

⇢ (x² + 10x +25) - 165²

⇢ x² = x²+ 10x + 25 - 165 = (140)

⇢ x² - 140 = x² - 10x

⇢ x²- x² - 140 = -10x

⇢ -140 = -10x

Now,

⇢ 140 = 10x

⇢ x = 140/10 = 14

⇢ 165 m

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Therefore, 165 meter is the area of the lawn.