The length of a room is three times its breadth and its volume is 240 m. The cost of plastering its four walls at Rs. 50 per square meter is Rs. 8000, find the height of the room. (Ans: 5 m)

Now, the cost of plastering it's 4 walls is Rs 8000 at the rate of 50 /m². So, we can find the area of the walls of the room by dividing 8000 by 50 i.e:

➙ A = Total cost / cost per m²

➙ 8000 / 50

➙ 800 / 5

➙ 160m²

In a cuboid , there are a pair of two opposite and equal rectangular sides, and area of rectangle is given by :

l × b

So, area of 2 walls along length :

➙ 2 × length × height

➙ 2 × 3x × h

➙ 6xh

Area of 2 walls along breadth:

➙ 2 × breadth × height

➙ 2 × x × h

➙ 2xh

Sum of areas of these four walls will be equal to the area of the walls, that we have find earlier;

➙ ( 6xh ) + ( 2xh ) = 160

➙ 8xh = 160

➙ xh = 160 / 8

➙ xh = 20 ‎ㅤ‎ㅤ‎ㅤ⸻ ( 2 )

Using equation ( 1 )

➙ 240 = 3x²h

➙ x²h = 240 / 3

➙ x × xh = 80

➙ x × 20 = 80 ‎ㅤ‎[ from equation ( 2 ) ]

➙ x = 80 / 20

➙ x = 4

Using equation ( 2 )

➙ xh = 20

➙ 4 × h = 20

➙ h = 20 / 4

➙ h = 5

‎ㅤ‎ㅤ‎ㅤ‎ㅤ‎ㅤ~Hence, the height of the room is 5m.

The length of a room is three times its breadth and its volume is 240 m. The cost of plastering its four walls at Rs. 50 per square meter is Rs. 8000, find the height of the room. (Ans: 5 m)​

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The length of a room is three times its breadth and its volume is 240 m. The cost of plastering its four walls at Rs. 50 per square meter is Rs. 8000, find the height of the room. (Ans: 5 m)