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

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