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

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

∵ 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

361 cm2
125 cm2
236 cm2
486 cm2

Correct Answer: 236 cm2

Explanation:

∵ 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

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