The sun of length, breadth and depth of a cuboid is 19

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The sun of length, breadth and depth of a cuboid is 19 cm and its diagonal is 5 √5 cm. Its surface area is?

1. 361 cm²
2. 125 cm²
3. 236 cm²
4. 486 cm²

Correct Option: C

∵ l + b + h = 19
and l² + b² + h² = (5√5)² = 125
∵ (l + b + h)² = (19)²
⇒ (l² + b²+ h²) + 2(lb + bh + lh) = 361
⇒ 2 (lb + bh + lh) = (361 - 125) = 236
∴ Surface area = 236 cm²