Question

In triangle abc ab =3cm bc=4. Bd is perpendicular to ac. Find bd if ac=5cm

Answer 1

Answer: 12/5 cm

Step-by-step explanation

By converse of pythagoras theorem

Angle B is 90°

Since AB^2 + BC^2= AC^2

In triangle ABC and Triangle BDC

Angle ABC = Angle BDC = 90°

since BD is perpendicular to AC angle BDC=90°

Angle ACB = Angle BCD common

Therefore triangle ABC is similar to triangle BDC

By AA similarity

Therefore

AB /BD = BC/DC= AC/BC by CPST

AB/BD = AC/BC

3/BD = 5/4

5BD = 12

BD = 12/5cm