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If two adjacent sides of a rectangular parallelopiped are 1 cm and 2 cm and the total surface area of the parallelopiped is 22 square cm, then the diagonal of the parallelopiped is
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- √10 cm
- 2√3 cm
- √14 cm
- 4 cm
- √10 cm
Correct Option: C
Let the third side of the rectangular parallelopiped be x cm, then
2 (x × 1 + 1 × 2 + 2 × x) = 22
⇒ 3x + 2 = 11
⇒ 3x = 11 – 2 = 9
Diagonal = √l² + b² + h²
= √3² + 2² + 1²
= √9 + 4 + 1
= √14 cm
