RD Sharma Solutions Chapter 4 Triangles Exercise 4.2 Class 10 Maths
Chapter Name  RD Sharma Chapter 4 Triangles 
Book Name  RD Sharma Mathematics for Class 10 
Other Exercises   Exercise 4.1
 Exercise 4.3
 Exercise 4.4
 Exercise 4.5
 Exercise 4.6
 Exercise 4.7

Related Study  NCERT Solutions for Class 10 Maths 
Exercise 4.2 Solutions
1. In △ABC, D and E are points on the sides AB and AC respectively such that DE BC
(i) If AD = 6 cm, DB = 9 cm and AE = 8 cm, find AC.
(ii) If AD/DB = 3/4 and AC = 15cm, find AE
(iii) If AD/DB = 2/3 and AC = 18cm, find AE
(iv) If AD = 4, AE = 8 , DB = x  4, and EC = 3x  19, find x.
(v) If AD = 8 cm, AB = 12 cm and AE = 12 cm, find CE.
(vi) If AD = 4cm, DB = 4.5 cm and AE = 8 cm, find AC.
(vii) If AD = 2cm , AB = 6 cm and AC = 9 cm, find AE.
(viii) If AD/BD = 4/5 and EC = 2.5 cm, find AE
(ix) If AD = x, DB = x  2, AE = x + 2 and EC = x  1, find the value of x.
(x) If Ad = 8x  7, DB = 5x  3, AE = 4x  3 and EC = (3x  1), find the value of x.
(xi) If AD = 4x  3, AE = 8x  7, BD = 3x  1 and CE = 5x  3, find the volume of x.
(xii) If AD = 2.5 cm, BD = 3.0 cm and AE = 3.75 cm, find the length of AC.
Solution
(i) If AD = 6 cm, DB = 9 cm and AE = 8 cm, find AC.
(ii) If AD/DB = 3/4 and AC = 15cm, find AE
(iii) If AD/DB = 2/3 and AC = 18cm, find AE
(iv) If AD = 4, AE = 8 , DB = x  4, and EC = 3x  19, find x.
(v) If AD = 8 cm, AB = 12 cm and AE = 12 cm, find CE.
(vi) If AD = 4cm, DB = 4.5 cm and AE = 8 cm, find AC.
(vii) If AD = 2cm , AB = 6 cm and AC = 9 cm, find AE.
(viii) If AD/BD = 4/5 and EC = 2.5 cm, find AE
(ix) If AD = x, DB = x  2, AE = x + 2 and EC = x  1, find the value of x.
(x) If Ad = 8x  7, DB = 5x  3, AE = 4x  3 and EC = (3x  1), find the value of x.
(xi) If AD = 4x  3, AE = 8x  7, BD = 3x  1 and CE = 5x  3, find the volume of x.
(xii) If AD = 2.5 cm, BD = 3.0 cm and AE = 3.75 cm, find the length of AC.
2. In a Î”ABC, D and E are points on the sides AB and AC respectively. For each of the following cases show that DEBC :
(i) AB = 2 cm, AD = 8cm, AE = 12cm and AC = 18 cm.
(ii) AB = 5.6 cm, AD = 1.4cm, AC = 7.2cm and AE = 1.8 cm.
(iii) AB = 10.8 cm, BD = 4.5 cm, AC = 4.8 cm and AE = 2.8 cm.
(iv) AD = 5.7 cm, BD = 9.5 cm, AE = 3.3 cm and EC = 5.5 cm
Solution
(i) AB = 2 cm, AD = 8cm, AE = 12cm and AC = 18 cm.
(ii) AB = 5.6 cm, AD = 1.4cm, AC = 7.2cm and AE = 1.8 cm.
(iii) AB = 10.8 cm, BD = 4.5 cm, AC = 4.8 cm and AE = 2.8 cm.
(iv) AD = 5.7 cm, BD = 9.5 cm, AE = 3.3 cm and EC = 5.5 cm
3. In a Î”ABC, P and Q are points on sides AB and AC respectively, such that PQ  BC. If AP = 2.4 cm, AQ = 2 cm, QC = 3 cm and BC = 6cm, find AB and PQ.
Solution
Hence, AB = 6cm and PO = 2.4 cm
4. In a Î”ABC, D and E are points on AB and AC respectively such that DE  BC. IF AD = 2.4 cm, AE = 3.2 cm, DE = 2 cm and BC = 5cm, find BD and CE.
Solution
5. In below Fig., state if PQ  EF. SolutionWe have,
DP = 3.9 cm , PE = 3 cm, DQ = 3.6 cm and QF = 2.4 cm
6. M and N are points on the sides PQ and PR respectively of a △PQR. For each of the following cases, state whether MN  QR
(i) PM = 4cm , QM = 4.5 cm, PN = 4cm and NR = 4.5 cm
Solution
7. In three line segments OA, OB and OC, points L, M, N respectively are so chosen that LM  AB and MNBC but neither of L, M, N nor of A, B, C are collinear. Show that LNAC. Solution
8. IF D and E are points on sides AB and AC respectively of a ∆ABC such that DE  BC and BD = CE. Prove that Î”ABC is isosceles.
Solution