If the sum of three dimensions and the total surface area

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If the sum of three dimensions and the total surface area of a rectangular box are 12 cm and 94 cm² respectively, then the maximum length of a stick that can be placed inside the box is

1. 5√2 cm
2. 5 cm
3. 6 cm
4. 2√5cm

Correct Option: A

Let the length, breadth and height of the box be x, y and z cm respectively.
∴ x + y + z = 12 ...(i)
and 2 (xy + yz + zx) = 94 ...(ii)
∴ (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx
⇒ 144 = x² + y² + z² + 94
→ x² + y² + z² = 144 – 94 = 50
∴ Maximum length of stick = √x² + y² + z²
= √50 = 5√2cm