Question

Length and breadth of a hall are in ratio of 6 : 4. The sum of area of roof and floor is equal to the area of all
walls together. If the volume of hall is 1200 m . Then length of hall is how much more than breadth?

Answer 1

See the attachment for detail solution

Answer 2

Answer:

Here, Length and breadth of a hall are in ratio of 6 : 4,

Let the length of the room = 6x,

Breadth of the room = 4x

Where x is any number,

Now, let h be the height of the room,

According to the question,

The sum of area of roof and floor is equal to the area of all  walls together.

6x × 4x + 6x × 4x = 2× 6x × h + 2× 4x × h

⇒ 24 x² + 24 x² = 12 xh + 8 xh

⇒ 48 x² = 20xh ⇒ h = 2.4 x

Hence, the volume of the room = 6x × 4x × 2.4x = 57.6 x³

Again according to the question,

57.6 x³ = 1200

⇒ x³ = 1200/57.6

⇒ $x=(\frac{125}{6})^{\frac{1}{3}}$

Hence, the difference between length and breadth = 6x - 4x = 2x

$=2\times (\frac{125}{6})^{\frac{1}{3} }=\frac{10}{6^{\frac{1}{3}}}$