Discussion

Explanation:

Ratio of the three diagonals is 3 : 2√3 : √15

Let the legths of the three diagonals be 3k, (2√3)k and (√15)k.

And, the brick have length, breadth, height as x, y and z respectively. 
 
∴ x² + y² = (3k)² = 9k² ...(1)

y² + z² = [(2√3)k]² = 12k² ...(2)

z² + x² = [(√15)k]² = 15k² ...(3)

Adding (1), (2) and (3), we get;
 
x² + y² + z² = 18k² ...(4)

Using (4) along with any of (1), (2) and (3), we get;

x = k√6 , y = k√3 and z = 3k, 

Required ratio = (k√3)/3k = 1/√3.

Hence, option (c).

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