Q. 513.7( 3 Votes )

A line segment 56cm long is to be divided into two parts in the ratio of 2:5. Find the length of each part.

Answer :


Consider AB as the segment having length 56 cm


Let C be the point which divides the segment AB in ratio 2:5 and the two parts as AC and CB


Let AC = a, from figure we have AB = AC + CB


56 = a + CB


CB = 56 – a


Now given is AC:BC = 2:5


=


=


cross multiply


(56 – a) × 2 = 5 × a


112 – 2a = 5a


112 = 5a + 2a


112 = 7a


a =


a = 16


Therefore AC = a = 16 cm and CB = 56 – a = 56 – 16 = 40 cm


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