Question

a square lawn is surrounded by a path 2m wide.ifthe area of the path is 240m,find the area of lawn

Answer 1

Let the side of lawn be a m
Area of lawn = a^2
Length of Outer side = (a+4) m
Area of outer square = (a+4)^2
= a^2 + 16 + 8a

Area of path = Area of outer square - Area of lawn
240 = a^2 +16 + 8 a - a^2
=> 240 = 8a + 16
=> 8(a+2) = 240
=> a+2 = 30
=> a= 28 m

Side of lawn = 28 m

Area of lawn = 28 * 28
= 784 m^2

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