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