Find two similar triangles with sides (A,B,C) and (A,B,D), such that D-C=20141.
If (A,B,C) is similar to (A,B,D) and D>C then C must be the smallest side of the first riangle and D = C+20141 the largest side of the second.
Without loss of generality, let B>A then we have the proportions
A B C
-- = ----------- = --
B C+20141 A
cross multiplying the first two and last two yields
B^2 = A(C+20141) and AB = C(C+20141)
solve the first for A and substitute into the second to get
B^3 = C(C+20141)(C+20141)
B = cu.rt.(C^3 + 40282C^2 + 405659881C)
I haven't found an integer solution (if there are any), but any value of C yield a solution that works.
C=5000, B=14675.0086804, A=8565.923383, D=25141
A/B = .5837082328
My guess is there is an integer solution which requires D-C to be so large, but I haven't found it yet.
Posted by Jer
on 2005-06-20 17:56:51