Question

Can a triangle be constructed with sides of given lengths?

$4,5,10$

Answer 1

According to triangles inequality, the sum of two sides of a triangle should be greater than the third side.

By taking two sides at a time, let's verify triangles inequality for a triangle having sides $4,5,10$

$$\begin{gathered} 4+5=9<10 \\ 4+10=14>5 \\ 5+10=15>4 \end{gathered}$$

Since, the above sides does not satisfy the triangles inequality,

Therefore the triangle cannot be constructed.