SOLUTION: ratio of length,breath and height of a room is 5:4:2. If area of four walls is 144 sq. metres.Find diagonal of the room?

Question 980028: ratio of length,breath and height of a room is 5:4:2. If area of four walls is 144 sq. metres.Find diagonal of the room?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
ratio to add to 144 is some x, 5x:4x:2x ;; x units are meters.
One pair of walls has area 2*10x^2)=20x^2 m^2
The other pair of walls has area 2*8x^2=16x^2 m^2
If x=2, one pair has area 80; the other has area 64 m^2
Therefore the ratio in the room is 10:8:4 m.
The floor is 10 x 8 with diagonal sqrt (100+64)=sqrt (164). Don't reduce it.
The room diagonal uses the floor diagonal as one leg, and the height as a second leg. The diagonal across the room is the square root of each of those squared.
The first is 164, the height is 16, and their sum is 180.
Take the square root of (180 m^2), and the answer is 6 sqrt(5) m or 13.4 meters.
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