Question

The square lawn has a path 4m wide around it . the area of the path is 196sq m . find the side of the lawn

Answer 1

let side of a square be a

so, Area of square of side a = a²

The square lawn has a path 4m wide around it
so, side of square = 4 + a + 4 = a + 8

Area of square (square of a + 4m wide path) of (a+8) = (a+8)² = a² + 16a + 64

the area of the path is 196sq m

Area of path = Area of square (square of a + 4m wide path) of (a+8) + Area of square of side a
196 = a² + 16a + 64 - a²
196 = 16a + 64
16a = 196 - 64
16a = 132
a = 132/16
a = 8.25m

so, Side of square lawn is 8.25m

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