Question

can the sides of a triangle have lengths of 20, 21, and 29? if so, what kind of triangle is it? yes, acute yes, right yes, obtuse no

Explanation:

Step1: Check triangle - inequality theorem

The sum of any two sides of a triangle must be greater than the third side.
$20 + 21=41>29$, $20 + 29 = 49>21$, $21+29 = 50>20$. So, a triangle can be formed.

Step2: Determine the type of triangle

Use the Pythagorean - like relationship $a^{2}+b^{2}$ compared to $c^{2}$ (where $c$ is the longest side).
Calculate $a^{2}+b^{2}$: $20^{2}+21^{2}=400 + 441=841$.
Calculate $c^{2}$: $29^{2}=841$.
Since $20^{2}+21^{2}=29^{2}$, by the Pythagorean theorem, the triangle is a right - triangle.

Answer:

B. yes, right