Question

A square lawn is surrounded by a 5 m wide path if the area of the path is 400 m² find the area of the lawn

Answer 1

Answer:

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Answer 2

Given data : A square lawn is surrounded by a 5 m wide path if the area of the path is 400 m².

To find : The area of the lawn.

Solution : Let, side of square lawn be x. and shape of 5 m wide path be square.

Now,

• Area of the square lawn = side² = x² ----{1}
• Area of the path = 400 m²

and

➜ Total length of the lawn and path = x + 5 + 5 = x + 10

Now,

➜ Total area of the lawn and path = (length)² = (x + 10)²

➜ Total area of the law and path = x² + 2 * 10x + 10²

➜ Total area of the law and path = x² + 20x + 100

Now,

➜ Area of the lawn = Total area of the law and path - Area of the path

➜ x² = x² + 20x + 100 - 400

➜ 20x + 100 - 400 = x²/x²

➜ 20x - 300 = 1

➜ 20x = 300

➜ x = 300/20

➜ x = 30/2

➜ x = 15

Put value of x in eq.{1}

➜ Area of the square lawn = x²

➜ Area of the square lawn = 15²

➜ Area of the square lawn = 225 m²

Answer : Hence area of the lawn is 225 m².

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