Question

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

Answer 1

The perimeter of the rectangular hall $=250m$

The cost of painting the four walls at the rate of $Rs.10per{m}^2=Rs.15000$

Step 1: Find the area of the four walls.

Let the length, breadth, and height of the rectangular hall be $l,b,\&h$ respectively.

Area of $4$ walls$=2lh+2bh=2(l+b)h$

The perimeter of the floor of the hall $=2(l+b)=250m$

Therefore, the area of $4$ walls $=250h{m}^2$

Cost of painting per $1m^2=10rupees$

Cost of painting per $250h{m}^2=(250h\times 10)rupees=2500hrupees$

Step 2: Find the height of the hall.

The cost of painting for $4$ walls is $15000rupees$

$$\begin{gathered} \therefore 2500h=15000 \\ h=\frac{15000}{2500} \\ h=6 \end{gathered}$$

Hence, the height of the hall is $6m.$