The dimensions of a cuboid are in the ratio $3:2:1$ and its total surface area is $352 \text{ cm}^{2}$. Find…

The dimensions of a cuboid are in the ratio $3:2:1$ and its total surface area is $352 \text{ cm}^{2}$. Find its length.
  1. $6$ cm
  2. $12$ cm
  3. $18$ cm
  4. $8$ cm

Solution

Let $l=3k, b=2k, h=k$. TSA $= 2(6k^{2}+2k^{2}+3k^{2}) = 22 k^{2} = 352 \Rightarrow k^{2} = 16 \Rightarrow k = 4$. Length $= 3k = 12$ cm.

Asked in: IMO

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