• Skip to main content
  • Skip to secondary menu
  • Skip to primary sidebar
  • Skip to footer
  • RBSE Model Papers
    • RBSE Class 12th Board Model Papers 2022
    • RBSE Class 10th Board Model Papers 2022
    • RBSE Class 8th Board Model Papers 2022
    • RBSE Class 5th Board Model Papers 2022
  • RBSE Books
  • RBSE Solutions for Class 10
    • RBSE Solutions for Class 10 Maths
    • RBSE Solutions for Class 10 Science
    • RBSE Solutions for Class 10 Social Science
    • RBSE Solutions for Class 10 English First Flight & Footprints without Feet
    • RBSE Solutions for Class 10 Hindi
    • RBSE Solutions for Class 10 Sanskrit
    • RBSE Solutions for Class 10 Rajasthan Adhyayan
    • RBSE Solutions for Class 10 Physical Education
  • RBSE Solutions for Class 9
    • RBSE Solutions for Class 9 Maths
    • RBSE Solutions for Class 9 Science
    • RBSE Solutions for Class 9 Social Science
    • RBSE Solutions for Class 9 English
    • RBSE Solutions for Class 9 Hindi
    • RBSE Solutions for Class 9 Sanskrit
    • RBSE Solutions for Class 9 Rajasthan Adhyayan
    • RBSE Solutions for Class 9 Physical Education
    • RBSE Solutions for Class 9 Information Technology
  • RBSE Solutions for Class 8
    • RBSE Solutions for Class 8 Maths
    • RBSE Solutions for Class 8 Science
    • RBSE Solutions for Class 8 Social Science
    • RBSE Solutions for Class 8 English
    • RBSE Solutions for Class 8 Hindi
    • RBSE Solutions for Class 8 Sanskrit
    • RBSE Solutions

RBSE Solutions

Rajasthan Board Textbook Solutions for Class 5, 6, 7, 8, 9, 10, 11 and 12

  • RBSE Solutions for Class 7
    • RBSE Solutions for Class 7 Maths
    • RBSE Solutions for Class 7 Science
    • RBSE Solutions for Class 7 Social Science
    • RBSE Solutions for Class 7 English
    • RBSE Solutions for Class 7 Hindi
    • RBSE Solutions for Class 7 Sanskrit
  • RBSE Solutions for Class 6
    • RBSE Solutions for Class 6 Maths
    • RBSE Solutions for Class 6 Science
    • RBSE Solutions for Class 6 Social Science
    • RBSE Solutions for Class 6 English
    • RBSE Solutions for Class 6 Hindi
    • RBSE Solutions for Class 6 Sanskrit
  • RBSE Solutions for Class 5
    • RBSE Solutions for Class 5 Maths
    • RBSE Solutions for Class 5 Environmental Studies
    • RBSE Solutions for Class 5 English
    • RBSE Solutions for Class 5 Hindi
  • RBSE Solutions Class 12
    • RBSE Solutions for Class 12 Maths
    • RBSE Solutions for Class 12 Physics
    • RBSE Solutions for Class 12 Chemistry
    • RBSE Solutions for Class 12 Biology
    • RBSE Solutions for Class 12 English
    • RBSE Solutions for Class 12 Hindi
    • RBSE Solutions for Class 12 Sanskrit
  • RBSE Class 11

RBSE Solutions for Class 10 Maths Chapter 11 Similarity Ex 11.4

April 16, 2019 by Fazal Leave a Comment

RBSE Solutions for Class 10 Maths Chapter 11 Similarity Ex 11.4 is part of RBSE Solutions for Class 10 Maths. Here we have given Rajasthan Board RBSE Class 10 Maths Chapter 11 Similarity Exercise 11.4.

Rajasthan Board RBSE Class 10 Maths Chapter 11 Similarity Ex 11.4

Question 1.
Answer the following in True of False. And (RBSESolutions.com) justify your answer of possible :
(i) Ratio of corresponding sides of two similar triangles is 4 : 9 then ratio of areas of these triangles is 4 : 9.
(ii) In the triangles ABC and DEF if
\(\frac { ar.\triangle ABC }{ ar.\triangle DEF } =\frac { { AB }^{ 2 } }{ { DE }^{ 2 } } =\frac { 9 }{ 4 } \)
then ∆ABC = ∆DEF
(iii) The ratio of areas of two similar triangles is proportional to square of their sides.
(iv) If ∆ABC and ∆AXY are similar and their areas are equal then sides XY and BC may coincides.
Solution :
RBSE Solutions for Class 10 Maths Chapter 11 Similarity Ex 11.4 1
Ratio of corresponding sides are 3 : 2 where s for similarity its ratio is 1 : 1
So this statement is wrong.
(iii) Ratio of areas of two similar triangles (RBSESolutions.com) is equal to ratio of square of their corresponding sides.
Thus statement is false.
(iv) ∆ABC ~ ∆AXY
RBSE Solutions for Class 10 Maths Chapter 11 Similarity Ex 11.4 2
Similarly BC = XY and AC = AY
Thus, statement is true.

RBSE Solutions

Question 2.
If ∆ABC ~ ∆DEF and their (RBSESolutions.com) areas are 64 cm2 and 121 cm2 respectively. If EF = 15.4 cm
Solution :
∵ ∆ABC ~ ∆DEF (given)
∴ Ratio of areas of ∆
= ratio of squares of corresponding sides ∆
RBSE Solutions for Class 10 Maths Chapter 11 Similarity Ex 11.4 3
RBSE Solutions for Class 10 Maths Chapter 11 Similarity Ex 11.4 4

Question 3.
In the following figure, two (RBSESolutions.com) triangles ABC and DBC are formed on same base BC. If AD, BC intersect at point O then show that
\(\frac { ar.\left( ABC \right) }{ ar.\left( DBC \right) } \) = \(\frac { AO }{ DO }\)
Solution :
Given : ∆ABC and ∆DBC are two triangles on same base BC. AD, BC intersects each other at point O.
RBSE Solutions for Class 10 Maths Chapter 11 Similarity Ex 11.4 5
To prove : \(\frac { ar.\left( ABC \right) }{ ar.\left( DBC \right) } \) = \(\frac { AO }{ DO }\)
Construction : From vertices A and D draw AE ⊥ BC and DE ⊥ BC respectively.
Proof : From vertices A and D, AE ⊥ BC and DF ⊥ BC.
∴ ∠AEO = ∠DFO = 90°
In right angled ∆AEO and ∆DFO
∠AEO = ∠DFO (each 90°)
∠AOE = ∠DOF (vertically opposite angles)
By A-A Similarity criterion
∆AEO – ∆DFO
⇒ \(\frac { AE }{ DF }\) = \(\frac { AO }{ DO }\)
Now area of ∆ABC = \(\frac { 1 }{ 2 }\) BC × AE
and area of ∆DBC = \(\frac { 1 }{ 2 }\) BC × DF
RBSE Solutions for Class 10 Maths Chapter 11 Similarity Ex 11.4 6
from equation (i) and (ii)
\(\frac { ar.\left( ABC \right) }{ ar.\left( DBC \right) } \) = \(\frac { AO }{ DO }\)

Question 4.
Solve the following questions :
(i) In ∆ABC and DE || BC and AD : DB = 2 : 3 then find (RBSESolutions.com) the ratio of areas of ∆ADE and ∆ABC.
(ii) PB and PA are perpendicular at A and B of line segment AB. If P and Q lies on two sides AB and by joining P and Q. It intersects AB at O and PD = 5 cm, QO = 7 cm, ar(∆POB) = 150 cm2 then find ar(∆QOA).
(iii) In figure, find x is terms of a, b and c
RBSE Solutions for Class 10 Maths Chapter 11 Similarity Ex 11.4 7
Solution :
(i) In ∆ABC BC || DE and \(\frac { AD }{ DB }\) = \(\frac { 2 }{ 3 }\) (given)
In ∆ABC and ∆DEA
∠B = ∠D
∠C = ∠E
RBSE Solutions for Class 10 Maths Chapter 11 Similarity Ex 11.4 8
A-A Similarity criterion
RBSE Solutions for Class 10 Maths Chapter 11 Similarity Ex 11.4 9
RBSE Solutions for Class 10 Maths Chapter 11 Similarity Ex 11.4 10
Thus, \(\frac { ar.\left( \triangle ADE \right) }{ ar.\left( \triangle ABC \right) } \) = \(\frac { 4 }{ 25 }\)
(ii) In ∆AOQ and ∆BOP
∠A = ∠B = 90° (given)
∠AOQ = ∠POB (vertically opposite angle)
RBSE Solutions for Class 10 Maths Chapter 11 Similarity Ex 11.4 11
(iii) ∠A = ∠B = 50° (corresponding angles)
∴ AE || BD
RBSE Solutions for Class 10 Maths Chapter 11 Similarity Ex 11.4 12
In ∆BDC and ∆AEC
∠A = ∠B = 50° (given)
∠E = ∠D (corresponding angles)
By AA similarity criterion
∆BDC ~ ∆AEC
∴ \(\frac { BC }{ AC }\) = \(\frac { BD }{ AE }\)
⇒ \(\frac { c }{ b+c }\) = \(\frac { x }{ a }\)
⇒ x = \(\frac { ac }{ b+c }\)

Question 5.
In ∆ABC, ∠B = 90° and BD is perpendicular (RBSESolutions.com) to hypotenuse AC then prove that
∆ADB ~ ∆BDC
Solution :
Given : In ∆ABC ∠B = 90° and BD ⊥ AC
To prove : ∆ADB ~ ∆BDC
RBSE Solutions for Class 10 Maths Chapter 11 Similarity Ex 11.4 13
In ∆ABC
∠A + ∠C = 90° [∵ ∠B = 90°] …..(i)
In ∆BDC
∠DBC + ∠C = 90° [∵ ∠BDC = 90°] ……(ii)
From equation (i) and (ii)
∠A + ∠C = ∠DBC + ∠C
⇒ ∠A = ∠DBC …(iii)
Now, In ∆ADB and ∆BDC
∠ADB = ∠BDC = 90° (given)
∠DAB = ∠DBC (by eqn(iii))
By A-A Similarly criterion
∆ADB ~ ∆BDC

RBSE Solutions

Question 6.
Prove that area of an equilateral triangle (RBSESolutions.com) formed any side of a square is half the area of an equilateral triangle formed at the diagonal of same square.
Solution :
Given : ABCD is a square whose our side is AB and diagonal is AC. An equilateral triangles ABE and ACE are formed on the sides AB and AC respectively.
RBSE Solutions for Class 10 Maths Chapter 11 Similarity Ex 11.4 14
To prove :
ar. (∆ABE) = ar. (∆ACF)
Proof : In right angle ∆ABC
AC2 = AB2 + BC2 (By Pythagoras theorem)
AC2 = AB2 + AB2 (∵ BC = AB)
AC2 = 2AB2
∴ AC = \(\sqrt { 2 }\) AB
Area of equilateral ∆ABE formed on side AB.
= \(\frac { { \left( AB \right) }^{ 2 }\sqrt { 3 } }{ 4 }\)
and area of equilateral ∆ACF formed on hypotenuse AC.
RBSE Solutions for Class 10 Maths Chapter 11 Similarity Ex 11.4 15
Thus (∆ABE) = \(\frac { 1 }{ 2 }\) ar.(∆ACF)

RBSE Solutions

We hope the given RBSE Solutions for Class 10 Maths Chapter 11 Similarity Ex 11.4 will help you. If you have any query regarding Rajasthan Board RBSE Class 10 Maths Chapter 11 Similarity Exercise 11.4, drop a comment below and we will get back to you at the earliest.

Share this:

  • Click to share on WhatsApp (Opens in new window)
  • Click to share on Twitter (Opens in new window)
  • Click to share on Facebook (Opens in new window)

Related

Filed Under: Class 10

Reader Interactions

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Primary Sidebar

Rajasthan Board Questions and Answers

Recent Posts

  • RBSE Class 9 Science Important Questions in Hindi & English Medium
  • RBSE Class 10 Maths Important Questions in Hindi & English Medium
  • RBSE Class 10 Science Important Questions in Hindi & English Medium
  • RBSE Class 9 Social Science Important Questions in Hindi & English Medium
  • RBSE Class 9 Social Science Notes in Hindi Medium & English Medium Pdf Download 2021-2022
  • RBSE Class 10 Social Science Important Questions in Hindi & English Medium
  • RBSE Solutions for Class 10 Maths Chapter 11 Constructions Ex 11.2
  • RBSE Solutions for Class 10 Maths Chapter 11 Constructions Ex 11.1
  • RBSE Class 10 Maths Important Questions Chapter 10 Circles
  • RBSE Solutions for Class 10 Maths Chapter 10 Circles Ex 10.2
  • RBSE Solutions for Class 10 Maths Chapter 10 Circles Ex 10.1

Footer

RBSE Solutions for Class 12
RBSE Solutions for Class 11
RBSE Solutions for Class 10
RBSE Solutions for Class 9
RBSE Solutions for Class 8
RBSE Solutions for Class 7
RBSE Solutions for Class 6
RBSE Solutions for Class 5
RBSE Solutions for Class 12 Maths
RBSE Solutions for Class 11 Maths
RBSE Solutions for Class 10 Maths
RBSE Solutions for Class 9 Maths
RBSE Solutions for Class 8 Maths
RBSE Solutions for Class 7 Maths
RBSE Solutions for Class 6 Maths
RBSE Solutions for Class 5 Maths
Target Batch
RBSE Class 11 Political Science Notes
RBSE Class 11 Geography Notes
RBSE Class 11 History Notes

Copyright © 2022 RBSE Solutions

 

Loading Comments...