The scenario from the given scenarios involving a right triangle is: "A triangular bike path with lengths of 5 miles, 12 miles, and 13 miles", as the sides satisfy the Pythagoras theorem.
When do three given line segments form a right triangle?
Any three line segments can form a right triangle only when they satisfy the Pythagoras Theorem, according to which, the square of the largest side in a right triangle is equal to the sum of the squares of the other two sides, that is, a² = b² + c², where a is the largest side, and b and c are the two other sides.
How to solve the given question?
In the question, we are asked to identify from the given scenarios, the case that involves a right triangle.
We know that for three segments to be a right triangle, they need to satisfy the Pythagoras Theorem. So we check every scenario with the theorem:
- A triangular bathroom tile with side lengths of 6 inches, 8 inches, and 12 inches: This is not a right triangle as it doesn't satisfy the Pythagoras theorem as (12² = 144) ≠ (6² + 8² = 36 + 64 = 100).
- A triangular bike path with lengths of 5 miles, 12 miles, and 13 miles: This is a right triangle as it satisfies the Pythagoras theorem as (13² = 169) ≠ (12² + 5² = 144 + 25 = 169).
- A triangular plot of land with side lengths of 10 yards, 10 yards, and 15 yards: This is not a right triangle as it doesn't satisfy the Pythagoras theorem as (15² = 225) ≠ (10² + 10² = 100 + 100 = 200).
- A triangular street sign with side lengths of 3 feet, 3 feet, and 3 feet: This is not a right triangle as it doesn't satisfy the Pythagoras theorem as all the sides are equal, so it is an equilateral triangle.
∴ The scenario from the given scenarios involving a right triangle is: "A triangular bike path with lengths of 5 miles, 12 miles, and 13 miles", as the sides satisfy the Pythagoras theorem.
Learn more about the Pythagoras Theorem at
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