Points P and Q are both in the line segment AB and on the same side of its midpoint. P divides AB in the ratio 2 : 3, and Q divides AB in the ratio 3 : 4. If PQ = 2, then find the length of the line segment AB.

Answer 1

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Answer 2

Label the points from left to right: A,P,Q,M,B

AP = 2x
PB = 3x
AQ = 3y
QB = 4y
PQ = 2

AP+PQ=AQ, so AQ-AP=PQ: 3y-2x = 2
PQ+QB=PB, so PB-QB=PQ: 3x-4y = 2

Solving that, we get y=2, so
AB = 7y = 14

Answer 3

Answer

Answer 4

P divides of the line AB=2:3

Q divides of line AB=3:4 

The distance between P and Q=2 cm

we have to find the length of AB=?

AB=AP+PB=2x+3x=5x

Or

AB=AQ+QB=3x+4x=7x

LCM of  5x and 7x=35x=AB

AP+PQ=AQ

2x+2=3x

x=2,

The length of AB=35×2 cm=70 cm