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) $A P<\quad(A B+A C+B C)$
(IMAGE TO BE ADDED)
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):
(IMAGE TO BE ADDED)
(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.
(IMAGE TO BE ADDED)
(i) A to D
(ii) From A to D , B and C
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