The length of the longest rod which can, be kept inside a rectangular box is 27 cm. If the length and the breadth of the box are 23 cm and 10 cm respectively, find its height.

10 cm

Given that the length of the longest rod = 27 cm.

Length of the box, l = 23 cm

Breadth of the box, b = 10 cm.

Let ‘h’ be the height of the box length of the longest rod

= Length of the diagonal = $\sqrt{l^2+b^2+h^2}⇒24=\sqrt{(23)^2+(10)^2+h^2}$

Squaring on both sides ⇒ $(27)^2=(23)^2+(10)^2+h⇒h=\sqrt{100}=10$

Hence, the height of the box = 10 cm