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

Answer: Option A

Let length = $$l$$, breadth = b, height = h
Given that
($$l$$ + b + h) = 12 cm
Total surface area of box
= 2($$l$$b + bh + h$$l$$)
= 94 m² (Given)
⇒ ($$l$$ + b + h)² = $$l$$² + b² + h² + 2($$l$$b + bh + h$$l$$)
⇒ (12)² = $$l$$² + b² + h² + 94
⇒ 144 - 94 = $$l$$² + b² + h²
⇒ 50 = $$l$$² + b² + h²
Diagonal of box $$=\sqrt{l^2+b^2+h^2}$$
∴ Length of longest rod that can be put inside the box
$$\begin{array}{rl}& =\sqrt{l^2+b^2+h^2}\\ & =\sqrt{50}\\ & =5\sqrt{2}\text{ cm}\end{array}$$