The length of a room is \frac{21}{16} times its breadth and breadth is \frac{4}{3} times its height. If H is the height of the room and L is the longest rod that can be placed in the room, then which one of the following is correct?

Explanation

Let height = H. Breadth B = \frac{4}{3}H. Length L_r = \frac{21}{16}B = \frac{21}{16} \times \frac{4}{3}H = \frac{7}{4}H. The longest rod is the body diagonal L = \sqrt{L_r^2 + B^2 + H^2} = \sqrt{(\frac{7}{4}H)^2 + (\frac{4}{3}H)^2 + H^2} = H \sqrt{\frac{49}{16} + \frac{16}{9} + 1} = H \sqrt{\frac{841}{144}} = \frac{29}{12}H. Therefore, 12L = 29H.

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