Provide detailed instructions how to construct a right triangle with edge lengths in geometric progression.

(In reply to

A Start by Kenny M)

I get this same result too:

Start with smallest side S, and coefficient a. Sides are S, a S, a^2 S

so, via Pythagorus: S^2 + a^2 S^2 = a^4 S^2

if b=a^2, and S^2 drops out, we have b^2 - b - 1 = 0.

The quadratic formula gives: b = [1 +/- SQRT(1 + 4)] /2

= 1/2 (+/-) SQRT(5)/2, while a = SQRT(b).

So a= 1.272..., or 0.786...

The 1st root is the right one to make the hypotenuse the largest side.

*(The second root, which is the reciprocal of the 1st, will satisfy the equation, but the three lengths can't make a triangle.)*

*Edited on ***September 5, 2018, 10:58 am**