Somehow, no more posts can be made to your thread on isosceles triangles

with same perimeter and area...

Your problem can be solved a bit easier by using 2 right triangles instead (half the isosceles):

Perimeters: a + c = d + f ; Areas: ab = deCode:D A e f b c C a B F d E

With the base ratio being 8:7, then follows that:

d = 7a/8, e = 8b/7, f = a + c - 7a/8

Now if you follow somewhat "Soroban's logic",

you'll find it all less wieldy...but still nothing "simple"!

Good way to start is using f's length:

a + c + 7a/8 = SQRT[(8b/7)^2 + (7a/8)^2]

Hope that helps; happy 2013!

Perhaps Soroban will comment...