Question

In a rectangular cuboid. the lengths of the diagonals on the three faces having a corner in common are 10, 12, 8 cm. What will be the length of the longest diagonal of the cuboid?
1. √168 cm
2. √178 cm
3. √154 cm
4. √150 cm

Answer 1

Correct Answer - Option 3 : √154 cm

Calculation:

A.T.Q

l² + b² = 100 

b² + h² = 144

h² + l² = 64

2 (l² + b² + h²) = 308

(l2 + b2 + h2) = 154

Largest diagonal = √l² + b² + h²  

⇒ √154 cm

∴ the length is √154 cm.