Question

A square plot has a 3m wide path surrounding it.If the area of the path is 132 Sq.m,find the area of the plot

Answer 1

Let the side of square plot be a m
Side of outer square = (a + 6) m

Area of square plot = a^2 m
Area of outer square = (a+6)^2
= a^2 +12a + 36 m^2


According to question
Area of path = 132
=> Outer Area - Area of plot = 132
=> a^2 +12a +36 - a^2 = 132
=> 12a + 36 = 132
=> 12a = 96
=> a = 8


Area of plot = 8^2
= 64 m^2

Answer 2

I hope it helps!
(We take y=x+6 because the side of the outer square exceeds the inner one by 6 units (3m+3m) )