Menelaus' Riddle

Geometry Level 5

Menelaus drew triangle ABCABC with BC=13BC = 13 before crossing two red lines BD=10BD = 10 and CE=15,CE = 15, both intersecting at point PP and reaching the triangle's sides at points DD and E,E, respectively, as shown above.

Menelaus: Mark this, lad. Point PP does not only divide all the red segments into integer lengths, but points DD and EE also divide the triangle's sides into integer lengths.

Pupil: O, so true, master! Any length between any two of those points is always a whole integer!

Menelaus: Then thou shalt tell me. What is the perimeter of triangle ABC?ABC?

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