SChand Composite Mathematics Class 7 Chapter 11 Triangle and it's Properties Exercise 11E

  Exercise 11 E

Question 1 

State with reasons , in which of the following cases triangle are not possible : 

$\triangle A B C, A B=7 \mathrm{~cm}, B C=3 \mathrm{~cm}, A C=8 \mathrm{~cm}$

$\triangle XYZ, XY=5 \mathrm{~cm}, YZ=12 \mathrm{~cm}, \quad XZ=7 \mathrm{~cm}$

$\triangle P Q R, \quad P Q=54 \mathrm{~m}, \quad Q R=105 \mathrm{~m}, \quad P R=45 \mathrm{~m}$

$\triangle L M N, \quad L M=3.9 \mathrm{~cm}, M N=4.1 \mathrm{~cm}, N L=6.8 \mathrm{~cm}$

$\triangle R S T  \quad R S=6.4 \mathrm{~cm}, \quad S T=2.9 \mathrm{~cm}, \quad R T=11.7 \mathrm{~cm}$

$\triangle D E F\quad D E=5.6 \mathrm{~cm}, E F=6.7 \mathrm{~cm}, D F=7.8 \mathrm{~cm}$

Question 2

O is any point within a $\triangle A B C$ Whose sides are 4cm, 5cm and 7 cm respectively prove that 

$(O A+O B+O C)>8 \mathrm{~cm}$

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Sol: $\triangle A O B$

$O A+O B>A B$...............(1)

$\triangle A O C$

$O A+O C>A C$.........(2)

$\triangle B O C$

$O B+O C>B C$ ........(3)

By adding (1)+ (2)+(3)

$O A+O B+O A+O C+O B+O C>A B+A C+B C$

$20 A+20 C+2 O B>4+5+7$

$2(O A+O B+O C)>16$

$O A+O B+O C>\frac{16}{2}$

$O A+O B+O C>8$

Question 3

In Triangle ABC, P is a point on the side BC. Complete each of the statements below using symbol 

'<" Or ">"  So as to make a true statements: 

(i) $A P<A B+B P$

(ii) $A P<A C+P C$

(iii) $A P<\quad(A B+A C+B C)$

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Question 4

P is a point is the interior of $\triangle A B C$ . State which of the following statements are true (T) or false (f): 

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(1) $A P+P B<A B$

(ii) $A P+P C>A C$

(iii) $B P+P C=B C$

Question 5

In the figure state which path is shorter. 

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(i) A to D 

 (ii) From A to D , B and C