# Geometry

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Is it possible for AB = 10, BC = 2x + 5 and AC = 5x, given that point B is the midpoint?

If you are talking about lengths of a line segment ABC, with B the midpoint, then

AB + BC = AC
15 + 2x = 5x
3x = 15
x = 3.
But also we must have
AB = BC for B to be a midpoint
10 = 2x + 5
x = 2

So no solution is possible.

• Geometry -

x=5

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