Question

Points P and Q are both on 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.
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Answer 1

Answer:

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