My Sum on Cevian Theorem

"In Δ ABC, B-P-C, BP = 4, PC = 8, A-Q-C, AQ = QC = 6. BQ intersects AP at point X. If CX is drawn and extended to intersect AB at point R , find length of PR.

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Triple Heronian Triangle with all the three integer sides and all the three corresponding integer heights (altitudes)

Is it possible to have a triangle with all three integer sides with their corresponding heights ( altitudes ) also integers. the answer is very much yes. I am dedicating this post to the memory of my parents, who selflessly loved and brought me up. Also due to the grace of Shree Akkalkot Swami Maharaj, Mahrashtra, India and Shree Gajanan MAharaj, Shegaon, MH, India I am able to make this post. Please find attached photos of MS Excel file that are self-explanatory. Actually I had lost the measures of the triangle that I made three years ago; but after praying to my Saints, now I can explain a method to form such many triangles. I am thankful to my above mentioned Sadguru Saints for this post. Please comment, suggest and correct me if I am wrong. Hemant Dikshit