A square plot has a 3m wide path surrounding it. If the area of the pa

1.	A square plot has a 3m wide path surrounding it. If the area of the path is 132sq.m, find the area of the plot.
Answer» QUESTION: A SQUARE plot has a 3m wide path surrounding it. If the area of the path is 132sq.m, find the area of the plot. solution: $\purple { \sf {64m}^{2} }$ GIVEN: A square plot has a 3m wide path surrounding it. If the area of the path is 132sq.m To find: find the area of the plot? step by step explanation: area of the plot = x given : area of the path = 132 sq.m area of the path = area of LARGE square - area of small square. $\sf let \: us \: assume \: small \: square \: as \: {x}^{2}$ $\sf let \: us \: assume \: large\: square \: as \: ({x + 6})^{2}$ so: $\sf {x}^{2} - ({x + 6}^{2} ) = 132$ $\sf {x}^{2} = ({x + 6}^{2} ) - 132$ $\sf \cancel{ {x}^{2}} = \cancel{{x}^{2} } + 12x + 36- 132$ $\sf96 = 12x$ $\sf x = 8$ therefore, $\red{ \sf area \: of \: small \: plot = 8×8 ={64m}^{2} }$