Question

A path $5cm$ wide runs along inside a square park of side $100cm$. Find the area of the path . Also find the cost of cementing at the rate of Rs $250$ per $10c{m}^2$.

Answer 1

Given: Outer side of square park, $s=100cm$

Area of outer square $=(side{)}^2={100}^2=10000c{m}^2$

width of path,$w=5cm$

Inner side of square $=100-5-5=90cm$

Area of inner square $={90}^2=8100c{m}^2$

Area of path $=$ Area of Outer square $-$ Area of inner square $=10000-8100=1900c{m}^2$

Cost of cementing $10c{m}^2$$=Rs.250$

Cost of cementing $1c{m}^2=\frac{250}{10}=Rs.25$

$\therefore$ Cost of cementing a $1900c{m}^2$ path $=Rs.1900\times 25=Rs.47500$