Discussion

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.

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