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June 8th, 2013, 01:57 PM   #1
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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?
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June 14th, 2013, 08:59 PM   #2
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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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