# The length of a hall is 18 m and the width 12 m.

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 hall.

Solution:

Length of the hall = 18 m

Width of the hall = 12 m

Now given,

Area of the floor and the flat roof = sum of the areas of four walls

⇒ 2∗lb = 2∗lh + 2∗bh

⇒ lb = lh + bh

$\Rightarrow \mathrm{h}=\frac{\mathrm{lb}}{\mathrm{l}+\mathrm{b}}$

$=\frac{18 * 12}{18+12}$

$=\frac{216}{30}=7.2 \mathrm{~m}$