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.

Answer 1

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,

$\red{ \sf area \: of \: small \: plot = 8×8 ={64m}^{2} }$

Answer 2

☆ Solution ☆

Given

• A square plot has a 3m wide path surrounding it. If the area of the path is 132sq.m

To Find

• The area of the plot.

Step-by-Step-Explaination

Let the side of square plot be 'x' m

Side of outer square = ( x + 6 ) m

Area of square plot = ${x}^{2}$ m

Area of outer square = $({x + 6})^{2}$

$= > {x}^{2} + 12x + {36m}^{2}$

According to the question

Area of path = 132

=> Outer Area - Area of plot = 132

$= > {x}^{2} + 12x + 36 - {x}^{2} = 132$

=> 12x + 36 = 132

=> 12x = 96

=> x = 8

$</p><p>Area \: of \: plot = {8}^{2}$

$=> {64}^{2}$