The length of the longest rod which can be kept inside a rectangular box is 17 cm. If the inner length and breadth of the box are 12 cm and 8 cm respectively, find its inner height.

The longest rod which can be kept inside a rectangular box will be equal to the diagonal of the box.

Let h cm be the inner height of box.

By formula,

Length of diagonal = $\sqrt{l^2 + b^2 + h^2}$

∴ 17 = $\sqrt{12^2 + 8^2 + h^2}$

Squaring both sides,

⇒ 17² = 12² + 8² + h²

⇒ 289 = 144 + 64 + h²

⇒ 289 = 208 + h²

⇒ h² = 289 - 208

⇒ h² = 81

⇒ h = $\sqrt{81}$ = 9 cm.

Hence, the inner height of rectangular box is 9 cm.