Segment BD by bisector of triangle ABC. Find: segments AD and DC, if AB = 10cm, BC = 15m, AC = 20m.

As we know from the school curriculum, the bisector will divide the side to which it is lowered in proportion to the two remaining sides.

Let the length of the segment AD be equal to the variable a.

Then the length of another segment can be represented as 20 – a.

Since we know the lengths of the other sides, it is possible to write down the equation and find out the lengths of AD and DC:

a / 10 = (20 – a) / 15;

3a / 30 = (40 – 2a) / 30;

5a = 40;

a = 8;

20 – 8 = 12.

Answer: The length of the segment AD will be 8 meters, and the length DC = 12.