Question

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

The value of '$\mathrm{a}$' is

• A. $5$
• B. $2$
• C. $7$
• D. $3$

Answer 1

The correct option is B

$2$

Step 1: Given data

Dimensions of a cuboidal box, $l=50cm$; $b=40cm$; $h=30cm$

Length of the longest rod that can be placed in the box$=50\sqrt{a}cm$

Step 2: Calculating the value of $a$

We know that length of the longest rod will have to be placed diagonally in the cuboidal box.

Thus, the length of the rod will be equal to the length of the diagonal of a cuboidal box.

Thus, the Length of the diagonal of a cuboidal box$=\sqrt{l^2+b^2+h^2}$

$\Rightarrow \sqrt{l^2+b^2+h^2}=\sqrt{{50}^2+{40}^2+{30}^2}=\sqrt{2500+1600+900}=\sqrt{5000}$$=50\sqrt{2}cm$\

Therefore, $a=2$

Hence, option B is correct.