Question

A square lawn is surrounded by a path $2$ m wide. If the area of the path is $240{\text{m}}^2$. Find the area of the 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$=(a+4{)}^2$

= $a^2+8a+16$

Area of the path = Area of outer sqare-Area of low

$\Rightarrow 240=a^2+8a+16-a^2$

$\Rightarrow 240=8a+16$

$\Rightarrow 8(a+2)=240$

$\Rightarrow a+2=\frac{240}{8}$

$\Rightarrow a+2=30$

$\Rightarrow a=30-2$

$\Rightarrow a=28$

side of lawn $=30$ m

Area of lawn = $28\times 28$

= $784m^2$