It is known that there are two points m and N on the line ab. point m divides AB into two parts 2:3 and point n divides AB into two parts 4:1. If Mn = 3cm, the length of AM and Nb can be obtained

It is known that there are two points m and N on the line ab. point m divides AB into two parts 2:3 and point n divides AB into two parts 4:1. If Mn = 3cm, the length of AM and Nb can be obtained

∵ point m divides AB into 2:3 parts, ∵ am = 25ab; ∵ point n divides AB into 4:1 parts, ∵ an-am = Mn, ∵ 45ab-25ab = 3, ∵ AB = 7.5cm, ∵ am = 25ab = 3cm. ∵ NB = ab-an = 15ab = 1.5cm. So am = 3cm, Nb = 1.5cm

It is known that M is the midpoint of AB, n is on MB, Mn = 3 / 5am, if Mn = 3cm, then AB = () cm

From Mn = 3 / 5am = 3 we know am = 5, from M is the midpoint of AB we know AB = 2am, so AB = 2 × 5 = 10

As shown in the figure, C is the midpoint of AB, n is the midpoint of BC, am is equal to one third of AC, Mn is known to be equal to 7cm, and the length of AB is calculated

A -- m -- C -- N -- B ∵ C is the middle point of ab ∵ AC = BC = AB / 2 ∵ n is the middle point of BC ∵ CN = BN = BC / 2 = (AB / 2) / 2 = AB / 4 ∵ am = AC / 3 ∵ am = (AB / 2) / 3 = AB / 6 ∵ cm = ac-am = AB / 2-AB / 6 = AB / 3 ∵ Mn = CN + cm = AB / 3 + AB / 4 = 7ab / 12 ∵ Mn = 7 ∵ 7ab / 12 = 7 ∵ AB = 12 (CM)