How do I do 448? Not sure how to find the lengths of the medians

Question

447.The sides of a triangle have lengths 9, 12, and 15. (This is a special triangle!)

(a) Find the lengths of the medians of the triangle.

(b) The medians intersect at the centroid of the triangle. How far is the centroid from each of the vertices of the triangle?

448.(Continuation) Apply the same questions to the equilateral triangle of side 6.

Answer 1

(a) 2(9² + 12²) = 15² + 4m₁²; m₁ = 7.5; 2(12² + 15²) = 9² + 4m₂²; m₂ = √657/2= 3√73/2

2(9² + 15²) = 12² + 4m₃²; m₃ = 3√13

(b) d₁ = 2/3·7.5 = 5; d₂ = 2/3·3√73/2 = √73; d₃ = 2/3·3√13 = 2√13

(c) m₁ = m₂ = m₃ = √(36 - 9) = 3√3; d₁ = d₂ = d₃ = 2/3·3√3 = 2√3.