Question

If the inner dimensions of a cuboidal box are 50 cm $\times$ 40 cm $\times$ 30 cm, then the length of the longest rod that can be placed in the box is

• A. $50\text{cm}$
• B. $50\sqrt{2}\text{cm}$
• C. $50\sqrt{3}\text{cm}$
• D. $120\text{cm}$

Answer 1

The correct option is B $50\sqrt{2}\text{cm}$

Length of the longest rod = length of diagonal


So, the length of the longest rod
$=\sqrt{l^2+b^2+h^2}=\sqrt{(50{)}^2+(40{)}^2+(30{)}^2}=\sqrt{5000}=\sqrt{2500\times 2}=50\sqrt{2}\text{cm}$