Question

The length of two sides of a triangle is 3 cm and 4 cm. Which of the following integral values can the third side take?

• A. $1$
• B. $4$
• C. $6$
• D. $7$

Answer 1

Answer: (B), (C)

The correct options are
B

$4$

C

$6$

$\text{Let the third side be x.}$

The third side of a triangle must be greater than the difference between the other two sides.

$\text{i.e., third side}>4-3$,
$\text{i.e.,}x>1$

Also, Sum of lengths of any two sides of a triangle is always greater than the third side.

$\text{i.e., third side}<3+4$,
$\text{i.e.,}x<7$

$\Rightarrow 1<x<7$

$\text{Hence, the integral values the third}\text{side, can take are 2, 3, 4, 5 and 6.}$