Question

the lengths of the sides ab, ac and bc of a triangle abc are 15cm,20cm and 28 cm respectively. x is a point on bc such that ax bisects angle a then bx=?

Answer 1

We can solve this question using the angle bisector theorem.

THEOREM:
Let the angle bisector of angle A intersect side BC at X between B and C. The angle bisector theorem states that the ratio of the line segment BX to the length of segment XC is equal to the ratio of AB to AC.

That is : BX / XC = AB / AC

CALCULATIONS :

Let BX = y then XC will be 20 - y

Substituting the values in the formula :

y / 20 - y = 15 / 28

15(20 - y) = y × 28

300 - 15y = 28y

300 = 43y

y = 300/43

y = 6.98 cm

Thus BX = 6.98cm