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If R is the midpoint of AB and S is the midpoint of BC and AS:SC=3:2, determine the length of BS if AC=50.

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I will assume that AC is the longest and B is between A and C
let AR = RB = x
let BS = SC = y

given: (2x+y)/y = 3/2
3y = 4x+2y
y = 4x

also : 2x + 2y = 50
x + y = 25
x + 4x = 25
x = 5

then BS = y = 4x = 20

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