The length of a hall is $18\ m$ and the width $12\ m$. The sum of the areas of the floor and the flat roof is equal to the sum of the areas of the four walls. Find the height of the hall.

Given:

The length of a hall is $18\ m$ and the width $12\ m$. The sum of the areas of the floor and the flat roof is equal to the sum of the areas of the four walls.

To do:

We have to find the height of the hall.

Solution:

Let $h$ be the height of the room.

Length of the room $(l) = 18\ m$

Width of the room $(b) = 12\ m$

Therefore,

Surface area of the floor and roof $= 2lb$

$= 2 \times 18 \times 12$

$= 432\ m^2$

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

$=2h(18 + 12)$

$= 2 \times 30h$

$= 60h\ m^2$

The surface area of the walls and the area of the floor and roof are equal.

This implies,

$60h = 432$

$h = \frac{432}{60}$

$= \frac{36}{5}\ m$

$=7.2\ m$

The height of the hall is $7.2\ m$.