RD Sharma Class 10 Solutions Chapter 4 Exercise 4.2 (Updated for 2021-22)

RD Sharma Class 10 Solutions Chapter 4 Exercise 4.2: In this exercise, the main focus is on similar triangles and their attributes. In the exercise problems, basic conclusions on proportionality and theorems are examined. Students can use the RD Sharma Class 10 Solutions to clarify their problems and as a study material for exams. Students can also use the RD Sharma Solutions for Class 10 Maths Chapter 4 Exercise 4.2 PDF provided below.

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RD Sharma Class 10 Solutions Chapter 4 Exercise 4.2

Access answers to RD Sharma Solutions Class 10 Maths Chapter 4 Exercise 4.2- Important Question with Answers

Question 1.
In an ∆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. (C.B.S.E. 1995)
(ii) If ADDB = 34 and AC = 15 cm, find AE. (C.B.S.E. 1994)
(iii) If ADDB = 23 and AC = 18 cm, find AE. (C.B.S.E. 1994C)
(iv) If AD = 4, AE = 8, DB = x – 4, and EC = 3x – 19, find x. (C.B.S.E. 1992C)
(v) If AD = 8 cm, AB = 12 cm and AE = 12 cm, find CE. (C.B.S.E. 1992C)
(vi) If AD = 4 cm, DB = 4.5 cm and AE = 8 cm, find AC. (C.B.S.E. 1992C)
(vii) If AD = 1 cm, AB = 6 cm and AC = 9 cm, findAE. (C.B.S.E. 1992C)
(viii) If ADDB = 45 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. (C.B.S.E. 1993C)
(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 value of x. (C.B.S.E. 2002)
(xii) If AD = 2.5 cm, BD = 3.0 cm and AE = 3.75 cm, find the length of AC. (C.B.S.E. 2006C)
Solution:

Question 2.
In a ∆ABC, D and E are points on the sides AB and AC respectively. For each of the following cases show that DE || BC:
(i) AB = 12 cm, AD = 8 cm, AE = 12 cm and AC = 18 cm. (C.B.S.E. 1991)
(ii) AB = 5.6 cm, AD = 1.4 cm, AC = 7.2 cm and AE = 1.8 cm. (C.B.S.E. 1990)
(ii) 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:
In ∆ABC, D and E are points on the sides AB and AC respectively
(i) AB = 12 cm, AD = 8 cm, AE = 12 cm and AC = 18 cm
DB = AB – AD = 12 – 8 = 4 cm and EC = AC – AE = 18 – 12 = 6 cm

Question 3.
In a ∆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 = 6 cm, find AB and PQ.
Solution:
In ∆ABC,
P and Q are points on AB and AC respectively such that PQ || BC
AP = 2.4 cm, AQ = 2 cm, QC = 3 cm and BC = 6 cm

Question 4.
In a ∆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 = 5 cm, find BD and CE. (C.B.S.E. 2001C)
Solution:
In the ∆ABC, DE || BC
AD = 2.4 cm, AE = 3.2 cm, DE = 2 cm and BC = 5 cm

Question 5.
In the figure, state if PQ || EF.

Solution:
In ∆DEF
PQ intersects DE and DF at P and Q respectively
Such that DP = 3.9 cm, PE = 3 cm DQ = 3.6 cm, QF = 2.4 cm

Question 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 = 4 cm, QM = 4.5 cm, PN = 4 cm, NR = 4.5 cm
(ii) PQ = 1.28 cm, PR = 2.56 cm, PM = 0.16 cm, PN = 0.32 cm
Solution:
(i) In the ∆PQR
M and N are points on PQ and PR respectively
PM = 4 cm, QM = 4.5 cm, PN = 4 cm, RN = 4.5 cm

Question 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:
Given: On OA, OB, and OC, points are L, M, and N respectively
Such that LM || AB, MN || BC

Question 8.
If D and E are points on sides AB and AC respectively of an ∆ABC such that DE || BC and BD = CE. Prove that ∆ABC is isosceles. (C.B.S.E. 2007)
Solution:
Given: In ∆ABC, D and E are points on the sides AB and AC such that BD = CD

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