Question

Can a triangle have three sides whose lengths are

$3cm,4cm,7cm?$

Answer 1

If the sum of two sides of a triangle is greater than the third side for all possible pairs only than a triangle is possible

Step 1 : Take any two sides, and check if the sum is greater than the third side

$3+7=10>4$

Step 2 : Repeat the process for all the other pairs

$$\begin{gathered} 4+7=11>3 \\ 3+4=7\ngtr 7 \end{gathered}$$

Since in the third pair $3+4=7\ngtr 7$the condition does not hold true

Hence the triangle is not possible