Question

Can the sides of a triangle have lengths 6, 15, and 20?

Answer 1

$\qquad \qquad\huge \underline{\boxed{\sf ᴀɴsweʀ}}$

Yes ! The given lengths can be sides of a triangle

Because :

1. sum of any two sides is smaller than the third side

that is ;

$\qquad \sf  \dashrightarrow \: 6 + 15 > 20$

$\qquad \sf  \dashrightarrow \: 6 + 20 > 15$

$\qquad \sf  \dashrightarrow \: 20 + 15 > 6$

and

2. Difference of any two sides is smaller than the third side :

$\qquad \sf  \dashrightarrow \: 15 - 6 < 20$

$\qquad \sf  \dashrightarrow \: 20 - 6 < 15$

$\qquad \sf  \dashrightarrow \: 20 - 15 < 6$