Question

If the length of sides of a right angle triangle are in arithmetic proportion propagation then find the ratio

Answer 1

Let one of the sides of the triangle be P.

Since the sides are in arithmetic progression, so other two sides will P + d and P + 2d, where d is the common difference.

Also since it is the right angled triangle, hypotenuse is the greatest side, so by Pythagoras theorem,
(P+2d)^2 = P^2 + (P+d) ^2

Solving the equation, we get d = P/3.

So the three sides are P, P+(P/3), P+2(P/3) or P, 4P/3 and 5P/3

Therefore the ratio between the sides is 3:4:5