Question

In a triangle ABC AB=3cm, BC=4cm, CA=4cm, then Semiparameters
5​

Answer 1

So, we have a Right Angled Triangle ABC, where AB = 3 cm, BC = 4 cm and AC = 5 cm (Angle B = 90 Degrees) and we want to find the length of BD, which is the perpendicular drawn from B on AC meeting AC at D.

There are several ways of going about it.

Using similar Triangles

Using Area of Triangle ABC in 2 ways

Using Area of Triangle ABC and Areas of Triangles ABD and BDC

With similar Triangles:

Triangle ABC is similar to Triangle ADB (Since corresponding angles are same).

Therefore BC / AC = DB / AB, so we have

4 / 5 = DB / 3

Thus DB (i. e. BD) = 4*3 / 5 = 2.4

Using Area of triangle ABC in 2 ways:

Area of Triangle ABC = 1/2 * Base * Height

= 1/2 * 4 * 3

= 6

Area of Triangle ABC is also equal to

1/2 * AC * BD

= 1/2 * 5 * BD

But we already know that it is 6, and equating (1/2 * 5)*BD with 6, we get BD = 12/5 = 2.4

Using Area of Triangle ABC and Areas of Triangles ABD and BDC:

This is pretty similar to 2 above, albeit a bit complex and this is being left as an exercise.

Thus, the required answer is 2.4