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How to do it? (Posted on 2018-09-05) Difficulty: 3 of 5
Provide detailed instructions how to construct a right triangle with edge lengths in geometric progression.

No Solution Yet Submitted by Ady TZIDON    
Rating: 5.0000 (1 votes)

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re: A Start- I concur | Comment 2 of 11 |
(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
  Posted by Steven Lord on 2018-09-05 10:50:28

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