Problem: Two medians of a triangle with unequal sides are 3 inches and 6 inches. Its area is 315β square inches. The length of the third median, in inches, is:
Answer Choices:
A. 4
B. 33β
C. 36β
D. 63β
E. 66β
Solution:
Figure ADBG is a parallelogram, so that AD=GB=4 and triangle ADMβ triangle BGM Area ΞADG= area ΞAMG+ area ΞMGB
= area ΞABG=31β area β³ABC
β΄31ββ 315β=(3+x)(3βx)(x+1)(xβ1)β,
15=(9βx2)(x2β1),x4β10x2+24=0
x2=4 or 6,x=2 or 6β. The value x=2 makes CM=6 and must be rejected since the given triangle is scalene. β΄CM=36β.
