. In triangle ABC, side AB has length 10, and the A- and B-medians have length 9 and 12, respectively. Compute the area of the triangle.

Answer 1

Draw a figure

Label the midpoint of BC as E and the midpoint of AC as f.

The intersection of the medians is P.

Length of BP = 8 and length PF = 4 because the intersection of the medians is at a point 2/3 of the distance from the vertex to the divided side; similarly length of AP = 6 and length of EP = 3.

Use the law of cosines to find the measure of angle APB; angle BPE is the supplement to angle APB.

Use angle angle BPE to compute the length of sides BC and AC.

Now you have the three sides of the triangle; use Heron's formula to compute the area.