Question

which real-world scenario involves a right triangle?

a triangular bathroom tile with side lengths of 6 inches, 8 inches, and 12 inches
a triangular bike path with lengths of 5 miles, 12 miles, and 13 miles
a triangular plot of land with side lengths of 10 yards, 10 yards, and 15 yards
a triangular street sign with side lengths of 3 feet, 3 feet, and 3 feet

Explanation:

Apply the Converse of the Pythagorean Theorem

$$ a^2 + b^2 = c^2 $$

Test each set of side lengths

$$
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$$

Identify the right triangle scenario

$$ 5^2 + 12^2 = 13^2 $$

Answer:

• (A) a triangular bathroom tile with side lengths of 6 inches, 8 inches, and 12 inches
• (B) a triangular bike path with lengths of 5 miles, 12 miles, and 13 miles (Correct answer)
• (C) a triangular plot of land with side lengths of 10 yards, 10 yards, and 15 yards
• (D) a triangular street sign with side lengths of 3 feet, 3 feet, and 3 feet