Question

The floor of a rectangular hall has a perimeter $250m$. If the cost of painting the four walls at the rate of Rs $10$ per $m^2$ is $15000$, find the height of the hall (in meters).

Answer 1

Given:

Perimeter$=250m$

$\Rightarrow$Area of $4$ walls $=2lh+2bh$

$=2(b+l)h$

$\Rightarrow$Perimeter of floor of wall $=2l+2b$

$\Rightarrow$$2(l+b)=250$ m

$\therefore$ Area of 4 walls $=2(l+b)h$

$=250h$ m${}^2$

$\Rightarrow$Cost of painting per $m^2$ area $=$ Rs. $10$

$\Rightarrow$Cost of painting $250h$ m${}^2$ area $=$ Rs$(250h\times 10)$

$=$ Rs.$2500h$

$\Rightarrow$Painting cost of walls $=$ Rs. $15000$

$\Rightarrow$$2500h=15000$

$\Rightarrow$$h=\frac{15000}{2500}$

$\Rightarrow$$h=6$m