Question

If side lengths $8\text{cm},5\text{cm}$ and $7\text{cm}$ are given can it form a triangle?

Answer 1

If $8\text{cm},5\text{cm}$ and $7\text{cm}$ are the sides of the triangle, then they should satisfy the inequality theorem. $AB+AC>BC$
$AB+BC>AC$ and
$BC+AC>AB$
Let $AB=8\text{cm},BC=5\text{cm}$ and $AC=7\text{cm}$
Then
$AB+BC>AC$
$8+5>7$
$\Rightarrow 13>7$
$BC+AC>AB$
$5+7>8$
$\Rightarrow 12>8$
$AB+AC>BC$
$8+7>5$
$\Rightarrow 15>5$
All the three conditions are satisfied, therefore a triangle can be formed with sides $8\text{cm},5\text{cm}$ and $7\text{cm}$