Medians DP and EQ of triangle DEF are perpendicular. If DP = 18 and EQ = 28, then what is DF?
+129852 D
Q
M
E P F
Let M be the intersection point of the two medians
By the property of medians DM = (2/3)18 = 12 MQ = (1/3) 28 = 28 / 3
So....since DP and EQ are perpendicular.....then DQ = sqrt [ 12^2 + (28/3)^2 ] =
sqrt [ 144 + 784/9 ] = sqrt [ 1296 + 784 ] / 3 = sqrt [ 2080 ] / 3 = 4sqrt (130) / 3
And DF = 2 DQ = 2 * 4sqrt (130) / 3 = (8/3)sqrt (130)
