The length of a rectangular room is double of its breadth and height is one third of the length . if the room contains 972 cubic meter of air,
find the area of floor of the room.

162 square meters

Step-by-step explanation:

Given: l=2b, which means b=l/2 (1)

           h=1/3l (2)

To find: Area of the floor (lxb)

Solution: Volume of air in the room=972 cubic meters

We know that volume of a cuboid = l x b x h

                                                    ⇒   972 = l x l/2 x l/3 (from (1) and (2))

                                                    ⇒   972 = l³/6

                                                    ⇒   l³ = 972 x 6

                                                    ⇒   l³ = 5832

                                                    ⇒   l = 18    

Substituting l = 18 in (1), we get b = 9

∴ l x b = 18 x 9

          = 162 square meters

Hence the area of the floor is 162 square meters.

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step-by-step explanation: