Question

BASIC GEOMET
66. Which of the following can not be the lengths
of the three sides of a triangle
(a) 6 cm, 7 cm, 12 cm
(b) 5 cm, 6 cm, 11 cm
(c) 4 cm, 5 cm, 7 cm
(d) None of these​

Answer 1

Answer:

b. 5 cm, 6 cm, 11 cm

Step-by-step explanation:

sum of two sides of a triangle is greater then the third one

So,

6 + 7 = 13 > 12

5 + 6 = 11 = 11

4 + 5 = 9 > 7

Answer 2

Answer : ↴

5 cm, 6 cm, 11 cm cannot be the lengths of the three sides of a triangle.

Formula used to solve this problem : ↴

$\boxed{ \sf \: Sum \: of \: 2 \: sides \: of \triangle \: \boxed {>} \: than \:the \: third \: side.}$

So, Let's find our answer now : ↴

$\sf \: (a) \: 6 \: cm, \: 7 \: cm, \: 12 \: cm$

$\sf \longrightarrow \: 6 \: + \: 7 \: = \: 13 \: \boxed {>} \: 12$

$\sf \longrightarrow \: 13 \: is \: more \: than \: 12$

$\sf \: So, \: this \: can \: be \: the \: lengths \: of \: the \: three \:sides \: of \: a \: \triangle.$

_____________________________

$\sf \: (b) \: 5 \: cm, \: 6 \: cm, \: 11 \: cm$

$\sf \longrightarrow \: 5 \: + \: 6 \: = \: 11 \: \boxed { = } \: 11$

$\sf \longrightarrow \: 11 \: is \: not \: more \: than \: 11.$

$\sf \: So, \: this \: cannot \: be \: the \: lengths \: of \: the \: three \:sides \: of \: a \: \triangle.$

_____________________________

$\sf \: (c) \: 4 \: cm, \: 5 \: cm, \: 7 \: cm$

$\sf \longrightarrow \: 4 \: + \: 5 \: = \: 9 \: \boxed { > } \:7$

$\sf \longrightarrow \: 9 \: is \: more \: than \: 7$

$\sf \: So, \: this \: can \: be \: the \: lengths \: of \: the \: three \:sides \: of \: a \: \triangle.$

_____________________________

$\sf \longrightarrow \: Hence \: B \: option \: is \: correct.$