Question

Can a triangle have three sides whose lengths are

$2.5cm,4.5cm,8cm?$

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

$4.5+8=12.5>2.5$

Step 2 : Repeat the process for all the other pairs

$$\begin{gathered} 2.5+8=10.5>4.5 \\ 2.5+4.5=7\ngtr 8 \end{gathered}$$

Since in the third pair $2.5+4.5=7\ngtr 8$ the condition does not hold true

Hence the triangle is not possible