Question

What kind of triangle is formed if the side lengths are 6, 7, and 8?
A. Acute
B. Obtuse
C. Right
D. No triangle can be formed with those side lengths.

Answer 1

Triangle Inequality for Existence

6 + 7 > 8 Yes
6 + 8 > 7 Yes
7 + 8 > 6 Yes

Definitely CAN be a triangle. Discard D.

Pythagorean Theorem

\(6^{2} + 7^{2} = 36 + 49 = 85 \ne 8^{2}\)

Definteily NOT a Right Triangle. Discard C.

Now what?