RD Sharma Solutions Chapter 4 Triangles Exercise 4.3 Class 10 Maths

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

  • Exercise 4.1
  • Exercise 4.2
  • Exercise 4.4
  • Exercise 4.5
  • Exercise 4.6
  • Exercise 4.7

Related Study

NCERT Solutions for Class 10 Maths

Exercise 4.3 Solutions

1. In a ΔABC, 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.


(iii) If AB = 3.5 cm , AC = 4.2cm  and DC = 2.8 cm, find BD.


= 7/3 = 2.33 cm 
∴ BD = 2.3 cm


(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 ΔABC, 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 . 

(viii) If AB = 10 cm, Ac = 6 cm and BC = 12 cm, find BD and DC. 

2. In Fig 4.57, AE is the bisector of the exterior ∠CAD meeting BC produced in E. If AB = 10cm, AC = 6cm and BC = 12cm, find CE. 
Solution

In ΔABC, 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. 


3. In Fig. 4.58, ΔABC is a triangle such that AB/AC = BD/DC, ∠B = 70°, ∠C = 50° . Find ∠BAD . 
Solution

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. 


4. In ΔABC (fig., 4.59), if ∠1 = ∠2,  prove that AB/AC = BD/DC . 
Solution


5. D, E and F are the points on sides BC, CA and AB respectively of ΔABC such that AD bisects ∠A, BE bisects ∠B and CF bisects ∠C. If AB = 5 cm, BC = 8 cm and CA = 4 cm, determine AP, CE and BD.
Solution

6. In fig., 4.60, check whether AD is the bisector of ∠A of ΔABC 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
Solution

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