Question

a square lawn has a 2 metre wide path surrounding it.If the area of the path is 136 m2,find the area of the lawn

Answer 1

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Answer 2

Step-by-step explanation:

Let ABCD be the square lawn and PQRS be the outer boundary of the square path.

Let the side of the lawn AB be x m.

Area of the square lawn = x²

Length PQ = (x m + 2 m + 2 m) = (x + 4) m

Area of PQRS = (x + 4)² = (x² + 8x + 16) m²

Now, Area of the path = Area of PQRS – Area of the square lawn

136 = x² + 8x + 16 – x²

136 = 8x + 16

136 – 16 = 8x

120 = 8x

x = 120/ 8 = 15

Side of the lawn = 15 m Hence, Area of the lawn = (Side)² = (15 m)² = 225 m²

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