Find x if DP= 4x-3 and CP=30
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In triangle ABC,segment BF is the angle bisector of angle ABC, segment AE,segment BF, and segment CD are medians, and P is the centroid. Find x if DP=4x-3 and CP=30
The centroid P is 2/3 of the way from C to D
so
(4x-3)2 = 30
8 x -6 = 30
8 x = 36
x = 36/8 = 9/2
so
(4x-3)2 = 30
8 x -6 = 30
8 x = 36
x = 36/8 = 9/2
The centroid divides a median in the ratio of 2:1, where the longer side is near the vertex, so
(4x-3) : 30 = 1 : 2
(4x-3)/30 = 1/2
8x - 6 = 30
8x = 36
x = 36/8 = 9/2 or 4.5
The fact that BF is the angle bisector was superfluous information and not needed. It merely shows that triangle ABC has to be isosceles, with BC = BA
(4x-3) : 30 = 1 : 2
(4x-3)/30 = 1/2
8x - 6 = 30
8x = 36
x = 36/8 = 9/2 or 4.5
The fact that BF is the angle bisector was superfluous information and not needed. It merely shows that triangle ABC has to be isosceles, with BC = BA
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