Question

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

given
AB divides of the line =AB=2:3
Q divides of line=AB=3:4The distance between P and Q=2cm
we have to find the length of AB=?AP=2x+3x=5x
AQ+QB=3x+4x=7x
LCM tx and 7x=35x
AP+PQ=AQ 2x+2x=3x
3x-2x=2xx=2x
the length of AB=3x35X2CM=70
ANS

Answer 2

Let the length of the line segment AB =x
given that
"P" divides the AB in the ratio=2:3
length of PA 2/5×x=2x/5
length of PQ=3/5×x=3x/5
and also given
Q divides AB in the ratio ,=3:4
lengthAB=3/4×x=3x/4
length AB =4/7×x=4x/7
therefore PQ=2CM[DATA]
AQ-AP=PQ=3x/7-2x/5=2
15x-14x÷35=2
x/35=2
x=2×35=70
length of the line segment =70