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`