3
QuizMultiple Choice

Pythagorean Inequalities

Question 3 • (Volch)WCA 3230 Geometry 3rd Nine Weeks 2025-2026

The sides of a triangle have lengths of x, x + 4, and 20. If the longest side is 20, which of the following values of x would make the triangle obtuse?

Answer
A
8
B
10
C
12
D
14

Explanation

For a triangle with longest side 20, the triangle is obtuse when 20² is greater than the sum of the squares of the other two sides. For x = 10, the other sides are 10 and 14, and 400 > 10² + 14² = 296. These lengths also form a triangle, so the correct choice is B, 10.

AI-written and checked against the verified answer.

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