A peacock is sitting on the top of a pillar, which is 9 m high. From a point 27 m away from the bottom of the pillar, a snake is coming to its hole at the base of the pillar. Seeing the snake the peacock pounces on it. If their speeds are equal, at what distance from the hole is the snake caught?

Let PH be the pillar.

Let the distance from the hole to the place where snake is caught = x m

Let P be the top of the pillar and S be the point where the snake is.

∴ SC = (27 – x) m

Given their speeds are equal.

So, SC = PC = (27 – x) m

Consider right angled ΔPHC,

By Pythagoras Theorem,

⇒ PH² + CH² = PC²

⇒ 9² + x² = (27 – x)²

⇒ 81 + x² = 729 – 54x + x²

⇒ 54x = 729 – 81 = 648

⇒ x = 648/54

∴ x = 12 m

Ans. The distance from the hole where the snake is caught is 12 m.