Question

The length of the longest pole(least integer) that can be kept inside a room of dimensions $12m\times 3\sqrt{3}m\times 3\sqrt{3}m$

• A. $10m$
• B. $12m$
• C. $16m$
• D. $14m$

Answer 1

The correct option is D $14m$

Consider the room to be a cuboid

The longest pole that can be put in will be the longest diagonal of a cuboid

The longest diagonal for a cuboid is given as

$\sqrt{(l^2+b^2+h^2)}$

$=\sqrt{{\left(12\right)}^2+{\left(3\sqrt{3}\right)}^2+{\left(3\sqrt{3}\right)}^2}$

$=\sqrt{144+9\times 3+9\times 3}$

$=\sqrt{144+27+27}$

$=\sqrt{198}$

$=14.07\approx 14m$