My Math Forum Triangular Fun!

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 June 8th, 2013, 12:57 PM #1 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,122 Thanks: 914 Triangular Fun! Code:  A G c e f h b B a C d D H g F Triangle ABD made up of 2 right triangles ABC and ADC. FGH is a right triangle. Perimeter a+c+d+e of ABD = perimeter f+g+h of FGH. Area b(a + d)/2 of ABD = area fg/2 of FGH. What are f and g in terms of a,b,c,d,e?
 June 14th, 2013, 07:59 PM #2 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,122 Thanks: 914 Re: Triangular Fun! Due to lack of interest(!), here's my solution: Let p = a+c+d+e and k = b(a+d). Then: g(+) ,f(-) = [p^2 + 2k +- SQRT(p^4 - 12kp^2 + 4k^2)] / (4p) Smallest case involving pythagorean triangles: a=9, b=12, c=15, d=16, e=20 ; f=15, g=20, h=25 : perimeter = 60, area = 150

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