The dimensions of a cuboid are in the ratio $5:4:3$ and its volume is $1620 \text{ cm}^{3}$. The length of…

The dimensions of a cuboid are in the ratio $5:4:3$ and its volume is $1620 \text{ cm}^{3}$. The length of the cuboid is:
  1. $9$ cm
  2. $15$ cm
  3. $12$ cm
  4. $18$ cm

Solution

Let $l=5k, b=4k, h=3k$. $V = 60 k^{3} = 1620 \Rightarrow k^{3} = 27 \Rightarrow k = 3$. Length $= 5k = 15$ cm.

Asked in: IMO

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