Question

If 4 cm and 7 cm are the lengths of two sides of a triangle, then the length of the third side may be ............

• A. 11 cm
• B. 3 cm
• C. 6 cm
• D. 12 cm

Answer 1

Answer: (C)

6 cm

$\Rightarrow$ The sum of the lengths of any two sides in a triangle is always greater than the length of the third side in the triangle.

$\Rightarrow$ The differnce of the lengths of any two sides in a triangle is always lesser than the length of the third side in the triangle.

$\Rightarrow$ The difference between $4cm$ and $7cm$ is

$3cm$ and their sum is $11cm$.

$\Rightarrow$ To ensure that the above mentioned rule is not violated, the possible length of the third side has got to be greater than $3cm$ and lesser than $11cm$.

$\Rightarrow$ So from the given options $6cm$ is less than

$11cm$ and greater than $3cm$

$\therefore$ The length of the third side of triangle is $6cm$