Problem: Two medians of a triangle with unequal sides are 3 inches and 6 inches. Its area is 315​ square inches. The length of the third median, in inches, is:
Answer Choices:
A. 4
B. 33​
C. 36​
D. 63​
E. 66​
Solution:
Figure ADBG is a parallelogram, so that AD=GB=4 and triangle ADM≅ triangle BGM Area ΔADG= area ΔAMG+ area ΔMGB
= area ΔABG=31​ area △ABC
∴31​⋅315​=(3+x)(3−x)(x+1)(x−1)​,
15=(9−x2)(x2−1),x4−10x2+24=0
x2=4 or 6,x=2 or 6​. The value x=2 makes CM=6 and must be rejected since the given triangle is scalene. ∴CM=36​.
