Bhaskara II Acharya/Lilavati/Chapter VI/150

: Chapter $\text {VI}$: Plane Figure: $150$

 * A snake's hole is at the foot of a pillar which is $15$ cubits high and a peacock is perched on its summit.
 * Seeing a snake, at a distance of thrice the pillar's height, gliding towards his hole, he pounces obliquely upon him.


 * Say quickly at how many cubits from the snake's hole do they meet, both proceeding an equal distance?

Solution
They meet $25$ cubits away from the pillar.

Proof
Let $y$ be the distance away from the snake's hole where they meet.

Let the peacock and snake move $x$ cubits.

Then:
 * $y = 45 = x$

The pillar, the ground and the flight of the peacock form a right triangle:
 * with legs of $15$ and $45 - x$
 * with hypotenuse $x$.

Hence:

It can be noted that the right triangle in question is the classic $\text {3-4-5}$ triangle expanded $5$ times.