RD Sharma Solutions Chapter 4 Triangles Exercise 4.3 Class 10 Maths
Chapter Name  RD Sharma Chapter 4 Triangles 
Book Name  RD Sharma Mathematics for Class 10 
Other Exercises 

Related Study  NCERT Solutions for Class 10 Maths 
Exercise 4.3 Solutions
1. In a Î”ABC, AD is the bisector of ∠A, meeting side BC at D.
(i) If BD = 2.5cm, AB = 5cm and AC = 4.2cm, find DC.
(ii) If BD = 2cm, AB = 5cm and DC = 3cm, find AC.
(iii) If AB = 3.5 cm , AC = 4.2cm and DC = 2.8 cm, find BD.
(iv) If AB = 10 cm, AC = 14cm and BC = 6cm, find BD and DC.
(v) If AC = 4.2cm, DC = 6 cm and 10cm, find AB
(vi) If AB = 5.6 cm, AC = 6cm and DC = 3 cm, find BC.
(vii) If AD = 5.6 cm, BC = 6cm and BD = 3.2cm, find AC.
(viii) If AB = 10 cm, Ac = 6 cm and BC = 12 cm, find BD and DC.
Solution
(i) If BD = 2.5cm, AB = 5cm and AC = 4.2cm, find DC.
(ii) If BD = 2cm, AB = 5cm and DC = 3cm, find AC.
(iv) If AB = 10 cm, AC = 14cm and BC = 6cm, find BD and DC.
(v) If AC = 4.2cm, DC = 6 cm and 10cm, find AB
We have,
BC = 10cm , DC = 6 cm and AC = 4.2cm
∴ BD = BC  DC = 10  6 = 4 cm
⇒ BD = 4cm
In Î”ABC, AD is the bisector of ∠A.
We know that, the internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.
(vi) If AB = 5.6 cm, AC = 6cm and DC = 3 cm, find BC.
(vii) If AD = 5.6 cm, BC = 6cm and BD = 3.2cm, find AC.
In ∆ABC, AD is the bisector of ∠A.
We know that, the internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the containing the angle .
In Î”ABC, AD is the bisector of ∠A.
We know that, the internal bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.
We have, if a line through one vertex of a triangle divides the opposite side in the ratio of the other two sides, then the line bisects the angle at the vertex.
6. In fig., 4.60, check whether AD is the bisector of ∠A of Î”ABC in each of the following :
(i) AB = 5cm, AC = 10cm, BD = 1.5cm and CD = 3.5cm
(ii) AB = 4cm, AC = 6 cm, BD = 1.6cm and CD = 2.4cm
(iii) AB = 8 cm, AC = 24 cm, BD = 6cm and BC = 24 cm
(iv) AB = 6cm, AC = 8cm , BD = 1.5cm and CD = 2cm.
(v) AB = 5cm, AC = 12cm, BD = 2.5cm and BC = 9 cm