+126 (1,7), (13,16) and (5,k) are the vertices of a triangle. What is the sum of all possible values of "k" for which the area of the triangle is minimum? (k can only be an integer)
+129847 Not totally sure about this one, geoNewbie, but here's what I get
We have a known (fixed) side that is 15 units in length { (1,7) to (13,16) } (5,k)
So one of these must be true
sqrt [ (1-5)^2 +(7-k)^2] + sqrt [ ( 13-5)^2 + (16-k)^2] > 15
sqrt [ ( 13 - 5)^2 + ( 16-k)^2 ] + 15 > sqrt [ ( 1-5)^2 + ( 7 - k)^2 ]
15 + sqrt [ ( 1-5)^2 + ( 7 - k)^2 ] > sqrt [ ( 13 - 5)^2 + ( 16-k)^2 ]
These are a little messy to solve, but using Wolframalpha, I only get a definite solution for the first
k < 10 or k > 10
So the points (5,9) and (5,11) seem to be the answers
Maybe someone else has a better solution ????
