What type of triangle is formed by sides of length 7, 8, and 13?
Answer: C
We use the converse of the Pythagorean theorem. Let c be the longest side.
If a² + b² > c², the triangle is acute.
If a² + b² = c², the triangle is right-angled.
If a² + b² < c², the triangle is obtuse.
Here, a=7, b=8, c=13.
a² + b² = 7² + 8² = 49 + 64 = 113.
c² = 13² = 169.
Since 113 < 169 (a² + b² < c²), the triangle is obtuse-angled.