Question

can the sides of a triangle have lengths of 17, 34, and 49? if so, what kind of triangle is it? yes, acute yes, right yes, obtuse no

Explanation:

Step1: Check triangle - inequality theorem

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
$17 + 34=51>49$, $17 + 49 = 66>34$, $34+49 = 83>17$. So, a triangle can be formed.

Step2: Determine the type of triangle

Let $a = 17$, $b = 34$, $c = 49$. Use the Pythagorean - related inequalities.
We check $a^{2}+b^{2}$ and $c^{2}$.
$a^{2}=17^{2}=289$, $b^{2}=34^{2}=1156$, $c^{2}=49^{2}=2401$.
$a^{2}+b^{2}=289 + 1156=1445$.
Since $a^{2}+b^{2}=1445<2401 = c^{2}$, by the Pythagorean - related inequality for obtuse - angled triangles ($a^{2}+b^{2}

Answer:

yes, obtuse