# The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of ₹ 10 per m^{2} is ₹ 15000, find the height of the hall. [Hint : Area of the four walls = Lateral surface area.]

**Solution:**

Given: The perimeter of the floor of the rectangular hall is 250m and the cost of painting the four walls at the rate of ₹10 per m² is ₹15000.

The area of the four walls of the cuboidal room will be the Lateral surface area of the cuboid.

Lateral surface area of cuboid = 2(l + b)h

The area of the four walls can also be obtained by dividing the total cost of the painting by the rate of painting per m^{2}.

Let the length, breadth, and height of the room be l, b, and h respectively. The cost of painting the four walls is ₹15000.

The rate of painting is ₹10 / m^{2}

Perimeter of the floor = 250 m

Therefore, 2(l + b) = 250 m ------------ (1) [Since, perimeter of a rectangle = 2(l + b)

Now, Area of four walls = 15000/10 m^{2} = 1500 m^{2}

2(l + b)h = 1500 m^{2} [From equation(1)]

250 m × h = 1500 m^{2}

h = 1500 m^{2}/250 m = 6 m

Thus, the height of the hall is 6 m.

**Video Solution:**

## The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of ₹ 10 per m² is ₹ 15000, find the height of the hall. [Hint : Area of the four walls = Lateral surface area.]

### Class 9 Maths NCERT Solutions - Chapter 13 Exercise 13.1 Question 3:

**Summary:**

It is given that the floor of a rectangular hall has a perimeter 250 m and the cost of painting the four walls at the rate of ₹10 per m^{2} is ₹15000. We have found that the height of the hall is 6 m.