# triangle with given 2 medians and 1 side

I need help with this exercise I got.

We have a triangle with given medians ma=6, mb=9 and side (without given median on that side) c=6. What is the length of a and b and with what values of ma,mb and c we wouldn't have a solution?

I've came to the solution (using trigonometry) that a is around 6 and b 0,7 but I'm not sure of it.

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What is your method. We can use en.wikipedia.org/wiki/… –  lab bhattacharjee Mar 30 '14 at 10:10
I used cosine rule. –  Breldor Mar 30 '14 at 10:13

$$2b^2+2c^2-a^2 = 4m_a^2 = 144 \\ 2a^2+2c^2-b^2 = 4m_b^2 = 324$$
Subtract $2c^2=72$ from both sides and you get