Question:
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 wall.
Solution:
Length of the hall $=18 \mathrm{~m}$
Its width $=12 \mathrm{~m}$
Suppose that the height of the wall is $\mathrm{h} \mathrm{m}$.
Also, sum of the areas of the floor and the flat roof $=$ sum of the areas of the four walls
$\Rightarrow 2 \times($ length $\times$ breadth $)=2 \times($ length $+$ breadth $) \times$ height
$\Rightarrow 2 \times(18 \times 12)=2 \times(18+12) \times \mathrm{h}$
$\Rightarrow 432=60 \times \mathrm{h}$
$\Rightarrow \mathrm{h}=\frac{432}{60}=7.2 \mathrm{~m}$
$\therefore$ The height of wall is $7.2 \mathrm{~m} .$