RD Sharma Class 10 Solutions Chapter 4 Exercise 4.6 (Updated for 2021-22)

RD Sharma Class 10 Solutions Chapter 4 Exercise 4.6

RD Sharma Class 10 Solutions Chapter 4 Exercise 4.6: In this exercise, you’ll learn more about triangle similarity. The essential ideas covered in the exercise problems are other distinguishing features and the areas of two identical triangles. RD Sharma Class 10 Solutions has all of the solutions needed for quick reference and exam preparation. Students can also refer to the RD Sharma Solutions for Class 10 Maths Chapter 4 Exercise 4.6 PDF, which is available below.

Download RD Sharma Class 10 Solutions Chapter 4 Exercise 4.6 Free PDF

 


RD Sharma Class 10 Solutions Chapter 4 Exercise 4.6

Access answers to RD Sharma Solutions Class 10 Maths Chapter 4 Exercise 4.6- Important Question with Answers

Question 1.
Triangles ABC and DEF are similar.
(i) If area (∆ABC) = 16 cm², area (∆DEF) = 25 cm² and BC = 2.3 cm, find EF. (C.B.S.E. 1992)
(ii) If area (∆ABC) = 9 cm², area (∆DEF) = 64 cm² and DE = 5.1 cm, find AB.
(iii) If AC = 19 cm and DF = 8 cm, find the ratio of the area of two triangles. (C.B.S.E. 1992C)
(iv) If area (∆ABC) = 36 cm², area (∆DEF) = 64 cm² and DE = 6.2 cm, find AB. (C.B.S.E. 1992)
(v) If AB = 1.2 cm and DE = 1.4 cm, find the ratio of the areas of ∆ABC and ∆DEF. (C.B.S.E. 1991C)
Solution:
RD Sharma Class 10 Chapter 4 Triangles
Triangles Class 10 RD Sharma
RD Sharma Class 10 Solutions Triangles

Question 2.
In the figure, ∆ACB ~ ∆APQ. If BC = 10 cm, PQ = 5 cm, BA = 6.5 cm and AP = 2.8 cm, find CA and AQ. Also, find the area (∆ACB) : area (∆APQ).
RD Sharma Class 10 Solutions Chapter 4 Triangles
Solution:
RD Sharma Class 10 Pdf Chapter 4 Triangles
RD Sharma Solutions Class 10 Chapter 4 Triangles

Question 3.
The areas of two similar triangles are 81 cm² and 49 cm² respectively. Find the ratio of their corresponding heights, what is the ratio of their corresponding medians ?
Solution:
Areas of two similar triangles are 81 cm² and 49 cm²
The ratio of the areas of two similar triangles are proportion to the square of their corresponding altitudes and also squares of their corresponding medians
Ratio in their altitudes = √81 : √49 = 9 : 7
Similarly, the ratio in their medians = √81 : √49 = 9 : 7

Question 4.
The areas of two similar triangles are 169 cm² and 121 cm² respectively. If the longest side of the larger triangle is 26 cm, find the longest side of the smaller triangle.
Solution:
Triangles are similar Area of larger triangle = 169 cm²
and area of the smaller triangle =121 cm²
Length of longest sides of the larger triangles = 26 cm
Let the length of longest side of the smaller triangle = x
Learncbse.In Class 10 Chapter 4 Triangles

Question 5.
The areas of two similar triangles are 25 cm² and 36 cm² respectively. If the altitude of the first triangle is 2.4 cm, find the corresponding altitude of the other.
Solution:
Area of first triangle = 25 cm²
Area of second = 36 cm²
Altitude of the first triangle = 2.4 cm
Let altitude of the second triangle = x
The triangles are similar
Class 10 RD Sharma Solutions Chapter 4 Triangles

Question 6.
The corresponding altitudes of two similar triangles are 6 cm and 9 cm respectively. Find the ratio of their areas.
Solution:
Length of the corresponding altitude of two triangles are 6 cm and 9 cm
triangles are similar
RD Sharma Class 10 Pdf Free Download Full Book Chapter 4 Triangles

Question 7.
ABC is a triangle in which ∠A = 90°, AN ⊥ BC, BC = 12 cm and AC = 5 cm. Find the ratio of the areas of the ∆ANC and ∆ABC.
Solution:
In ∆ABC, ∠A = 90°
AN ⊥ BC
BC = 12 cm, AC = 5 cm
RD Sharma Class 10 Solution Chapter 4 Triangles

Question 8.
In the figure, DE || BC
(i) If DE = 4 cm, BC = 6 cm and area (∆ADE) = 16 cm², find the area of ∆ABC.
(ii) If DE = 4 cm, BC = 8 cm and area of (∆ADE) = 25 cm², find the area of ∆ABC. (C.B.S.E. 1991)
(iii) If DE : BC = 3 : 5, calculate the ratio of the areas of ∆ADE and the trapezium BCED
RD Sharma Class 10 Pdf Ebook Chapter 4 Triangles
Solution:
RD Sharma Class 10 Pdf Ebook Chapter 4 Triangles
RD Sharma Class 10 Pdf Ebook Chapter 4 Triangles
RD Sharma Class 10 Pdf Ebook Chapter 4 Triangles

Question 9.
In ∆ABC, D and E are the mid-points of AB and AC respectively. Find the ratio of the areas of ∆ADE and ∆ABC.
Solution:
In ∆ABC, D and E are the mid points of AB and AC respectively
RD Sharma Maths Class 10 Solutions Pdf Free Download Chapter 4 Triangles

Question 10.
The areas of two similar triangles are 100 cm² and 49 cm² respectively. If the altitude of the bigger triangle is 5 cm, find the corresponding altitude of the other. (C.B.S.E. 2002)
Solution:
∆ABC ~ ∆DEF
area ∆ABC = 100 cm²
and area ∆DEF = 49 cm²
RD Sharma Class 10 Book Pdf Free Download Chapter 4 Triangles
Class 10 RD Sharma Chapter 4 Triangles

Question 11.
The areas of two similar triangles are 121 cm² and 64 cm² respectively. If the median of the first triangle is 12.1 cm, find the corresponding median of the other. (C.B.S.E. 2001)
Solution:
∆ABC ~ ∆DEF
area of ∆ABC = 121 cm² area of ∆DEF = 64 cm²
AL and DM are the medians of ∆ABC and ∆DEF respectively
AL = 12.1 cm
RD Sharma Maths Class 10 Solutions Chapter 4 Triangles

Question 12.
In ∆ABC ~ ∆DEF such that AB = 5 cm and (∆ABC) = 20 cm² and area (∆DEF) = 45 cm², determine DE.
Solution:
∆ABC ~ ∆DEF
area (∆ABC) = 20 cm²
area (∆DEF) = 45 cm²
RD Sharma 10 Class Solutions Chapter 4 Triangles
RD Sharma Class 10 Textbook PDF Chapter 4 Triangles

Question 13.
In ∆ABC, PQ is a line segment intersecting AB at P and AC at Q such that PQ || BC and PQ divides ∆ABC into two parts equal in area. Find BPAB.
Solution:
In ∆ABC, PQ || BC and PQ divides ∆ABC in two parts ∆APQ and trap. BPQC of equal in area
i.e., area ∆APQ = area BPQC
Maths RD Sharma Class 10 Solutions Chapter 4 Triangles
10th Maths Solution Book Pdf Chapter 4 Triangles

Question 14.
The areas of two similar triangles ABC and PQR are in the ratio 9 : 16. If BC = 4.5 cm, find the length of QR. (C.B.S.E. 2004)
Solution:
∆ABC ~ ∆PQR
area (∆ABC) : area (∆PQR) = 9 : 16
and BC = 4.5 cm
RD Sharma 10 Chapter 4 Triangles
RD Sharma Class 10 Book Pdf Chapter 4 Triangles

Question 15.
ABC is a triangle and PQ is a straight line meeting AB in P and AC in Q. If AP = 1 cm, PB = 3 cm, AQ = 1.5 cm, QC = 4.5 cm, prove that area of ∆APQ is one sixteenth of the area of ∆ABC. (C.B.S.E. 2005)
Solution:
In ∆ABC, P and Q are two points on AB and AC respectively such that
AP = 1 cm, PB = 3 cm, AQ = 1.5 cm and QC = 4.5 cm
Solution Of RD Sharma Class 10 Chapter 4 Triangles
RD Sharma 10 Solutions Chapter 4 Triangles

Question 16.
If D is a point on the side AB of ∆ABC such that AD : DB = 3 : 2 and E is a point on BC such that DE || AC. Find the ratio of areas of ∆ABC and ∆BDE. (C.B.S.E. 2006C)
Solution:
In ∆ABC, D is a point on AB such that AD : DB = 3 : 2
RD Sharma Maths Book For Class 10 Solution Chapter 4 Triangles

Question 17.
If ∆ABC and ∆BDE are equilateral triangles, where D is the mid point of BC, find the ratio of areas of ∆ABC and ∆BDE. [CBSE 2010]
Solution:
∆ABC and ∆DBE are equilateral triangles Where D is mid point of BC
RD Sharma Class 10 Maths Chapter 4 Triangles
RD Sharma Mathematics Class 10 Pdf Download Free Chapter 4 Triangles

Question 18.
Two isosceles triangles have equal vertical angles and their areas are in the ratio 36 : 25. Find the ratio of their corresponding heights.
Solution:
Two isosceles triangles have equal vertical angles
So their base angles will also be the equal to each other
Triangles will be similar Now, ratio in their areas = 36 : 25
Answers Of RD Sharma Class 10 Chapter 4 Triangles

Question 19.
In the figure, ∆ABC and ∆DBC are on the same base BC. If AD and BC intersect
Class 10 RD Sharma Pdf Chapter 4 Triangles
Solution:
Given : Two ∆ABC and ∆DBC are on the same base BC as shown in the figure
AC and BD intersect eachother at O
RD Sharma Class 10 Solutions Pdf Free Download Chapter 4 Triangles
RD Sharma Class 10 Solutions Pdf Free Download Chapter 4 Triangles

Question 20.
ABCD is a trapezium in which AB || CD. The diagonals AC and BD intersect at O. Prove that
(i) ∆AOB ~ ∆COD
(ii) If OA = 6 cm, OC = 8 cm, find
RD Sharma Mathematics Class 10 Pdf Download Free Chapter 4 Triangles
Solution:
Given : ABCD is a trapezium in which AB || CD
Diagonals AC and BD intersect each other at O
RD Sharma Maths Book For Class 10 Solution Chapter 4 Triangles
Solution Of RD Sharma Class 10 Chapter 4 Triangles

Question 21.
In ∆ABC, P divides the side AB such that AP : PB = 1 : 2. Q is a point in AC such that PQ || BC. Find the ratio of the areas of ∆APQ and trapezium BPQC.
Solution:
In ∆ABC, P is a point on AB such that AP : PQ = 1 : 2
PQ || BC
Now we have to find the ratio between area ∆APQ and area trap BPQC
RD Sharma 10 Chapter 4 Triangles
Maths RD Sharma Class 10 Solutions Chapter 4 Triangles

Question 22.
AD is an altitude of an equilateral triangle ABC. On AD as base, another equilateral triangle ADE is constructed. Prove that Area (∆ADE) : Area (∆ABC) = 3 : 4. [CBSE 2010]
Solution:
Given: In equilateral ∆ABC, AD ⊥ BC and with base AD, another equilateral ∆ADE is constructed
RD Sharma 10 Class Solutions Chapter 4 Triangles

We have provided complete details of RD Sharma Class 10 Solutions Chapter 4 Exercise 4.6. If you have any queries related to CBSE Class 10, feel free to ask us in the comment section below.

FAQs on RD Sharma Class 10 Solutions Chapter 4 Exercise 4.6

Is it important to study all of the concepts included in RD Sharma Class 10 Solutions Chapter 4 Exercise 4.6?

Yes, learning all of the concepts included in RD Sharma Solutions for Class 10 Maths Chapter 4 Exercise 4.6 is required in order to achieve high scores on the Class 10 board exams. These solutions were created by subject matter specialists who compiled model questions that covered all of the textbook’s exercise questions.

Where can I download RD Sharma Class 10 Solutions Chapter 4 Exercise 4.6 free PDF?

You can download RD Sharma Class 10 Solutions Chapter 4 Exercise 4.6 free PDF from the above article.

What are the benefits of using RD Sharma Class 10 Solutions Chapter 4 Exercise 4.6?

1. Correct answers according to the latest CBSE guidelines and syllabus.
2. The RD Sharma Class 10 Solutions Chapter 4 Exercise 4.6 is written in simple language to assist students in their board examination, & competitive examination preparation.

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