# 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 4.1Exercise 4.3Exercise 4.4Exercise 4.5Exercise 4.6Exercise 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 ΔABC, D and E are points on the sides AB and AC respectively. For each of the following cases show that DE||BC :
(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 ΔABC, 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

4. In a ΔABC, 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.
Solution

We 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 MN||BC but neither of L, M, N nor of A, B, C are collinear. Show that LN||AC.
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 ΔABC is isosceles.
Solution