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If the sum of the dimensions of a rectangular parallelopiped is 24 cm and the length of the diagonal is 15 cm, then the total surface area of it is
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- 420 cm²
- 275 cm²
- 351 cm²
- 378 cm²
- 420 cm²
Correct Option: C
Let, length = a cm.
breadth = b cm.
height = c cm.
∴ a + b + c = 24 --- (i)
and √a² + b² + c² = 15
⇒ a² + b² + c² = 15 × 15 = 225 - - - (ii)
∴ (a + b +c)² = a² + b² + c² + 2 (ab + bc + ca)
⇒ 24² = 225 + 2 (ab + bc + ca)
⇒ 576 = 225 + 2 (ab + bc + ca)
⇒ 2 (ab + bc + ca) = 576 – 225 = 351 sq.cm. = Total surface area
