A square park is surrounded by a path of uniform width 2 meters all around it. The area of the path is 288 sq. meters. Find the perimeter of the park.
Solution
Correct Answer: Option C
Let,one side of the park is x meter.
So, one side of the park with path = x + (2 + 2)
= x + 4
We know,
Area of the park = x2
Area of the path, (x + 4)2 - x2 = 288
⇒ x2 + 8x + 16 - x2 = 288
⇒ 8x + 16 = 288
⇒ 8x = 288 - 16
⇒ 8x = 272
⇒ x = 272/8
∴ x = 34
One side of the square = 34 m.
So, perimeter of the square =4 × 34
= 136 m
So, one side of the park with path = x + (2 + 2)
= x + 4
We know,
Area of the park = x2
Area of the path, (x + 4)2 - x2 = 288
⇒ x2 + 8x + 16 - x2 = 288
⇒ 8x + 16 = 288
⇒ 8x = 288 - 16
⇒ 8x = 272
⇒ x = 272/8
∴ x = 34
One side of the square = 34 m.
So, perimeter of the square =4 × 34
= 136 m
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