Question

Any Genius here......, Answer if any
Please. ​

Answer 1

A, B and C are the vertexes of ∆ ABC.

This should roughly be the figure... fig 1.

Expanding, we get ... fig 2.

After bouncing nine times, finally the ball hits a vertex B starting from A, Right top to left bottom of fig 2.

Each of the lengths, AB, AC are the sides of the equilateral triangle and are equal.

Angle of Incidence equals Angle of reflection.

Hence, fig 3...

All the triangles are congruent.

Distance travelled by ball is in form of √N, n is an integer.

From fig 1, suppose the ball moves 5.5 units horizontally, 3.5 units vertically.

{ Finding two numbers such that their sum is 9 and distance travelled is √N, N is an integer.

Use hidden trial. }

Hence, N = 31 units , √N = √ 31 units.

The answer is 31.

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