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Similar Sides Sought (Posted on 2005-06-20) Difficulty: 3 of 5
Find two similar triangles with sides (A,B,C) and (A,B,D), such that D-C=20141.

See The Solution Submitted by Old Original Oskar!    
Rating: 3.5000 (2 votes)

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General Solution | Comment 1 of 6

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.

For example

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
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