Q14 of 48 Page 101

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.

From the given, draw a line segment below

geogebra-export.png


Let the length of the line segment AB = X


P divides AB in the ratio = 2:3


Thus the length of AP =


The length of PB = AB-AP




∴PB


Q divides AB in the ratio = 3:4


Thus the length of AQ =


The length of QB = AB-AQ




∴QB


The length of PQ in the line segment = AQ-AP



by solving this,




Given, PQ = 2


∴


X = 35×2


∴X = 70


The length of the line segment AB is 70 cm


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