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

#### Complete Python Prime Pack for 2023

9 Courses     2 eBooks

#### Artificial Intelligence & Machine Learning Prime Pack

6 Courses     1 eBooks

#### Java Prime Pack 2023

8 Courses     2 eBooks

Given:

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

To do:

We have to find the height of the hall.

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

We know that,

The perimeter of the rectangle $=2(l+b)$

We have,

Area of the four walls = Lateral surface area and

The perimeter of the rectangle is $250\ m$.

Therefore,

The area of the wall $=2lh+bh$

This implies,

The area of the four walls $=2(l+b)h$

$=2(l+b)h$

$=250h\ m^2$

We also have,

The cost of painting the wall per square meter $=Rs.\ 10$

The cost of painting the four walls per square meter $=$ area of the four walls $\times$ the cost of painting the wall per square meter

This implies,

$=250h\ m^2\times Rs.\ 10$

$=Rs.\ 2500h\ m^2$

We have,

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

This implies,

$Rs.\ 15000=Rs.\ 2500h$

$h=\frac{Rs.\ 2500}{Rs.\ 15000}$

$h=6$

Therefore,

The height of the wall is $6\ m$.

Updated on 10-Oct-2022 13:42:09