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
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
Answers
GPT-4o mini
A right triangle is defined as a triangle that has one angle measuring 90 degrees. This can be identified using the Pythagorean theorem, which states that in a right triangle with legs a and b, and hypotenuse c, the relationship \(a^2 + b^2 = c^2\) holds true.
Let's analyze the given scenarios:
1. **Triangular bathroom tile:** Side lengths are 6 inches, 8 inches, and 12 inches.
- Check: \(6^2 + 8^2 = 36 + 64 = 100\) and \(12^2 = 144\). Not a right triangle.
2. **Triangular bike path:** Side lengths are 5 miles, 12 miles, and 13 miles.
- Check: \(5^2 + 12^2 = 25 + 144 = 169\) and \(13^2 = 169\). This is a right triangle.
3. **Triangular plot of land:** Side lengths are 10 yards, 10 yards, and 15 yards.
- Check: \(10^2 + 10^2 = 100 + 100 = 200\) and \(15^2 = 225\). Not a right triangle.
4. **Triangular street sign:** Side lengths are 3 feet, 3 feet, and 3 feet.
- Check: All sides are equal (equilateral), so it cannot be a right triangle.
The only right triangle among the provided scenarios is the **triangular bike path with lengths of 5 miles, 12 miles, and 13 miles**.
Let's analyze the given scenarios:
1. **Triangular bathroom tile:** Side lengths are 6 inches, 8 inches, and 12 inches.
- Check: \(6^2 + 8^2 = 36 + 64 = 100\) and \(12^2 = 144\). Not a right triangle.
2. **Triangular bike path:** Side lengths are 5 miles, 12 miles, and 13 miles.
- Check: \(5^2 + 12^2 = 25 + 144 = 169\) and \(13^2 = 169\). This is a right triangle.
3. **Triangular plot of land:** Side lengths are 10 yards, 10 yards, and 15 yards.
- Check: \(10^2 + 10^2 = 100 + 100 = 200\) and \(15^2 = 225\). Not a right triangle.
4. **Triangular street sign:** Side lengths are 3 feet, 3 feet, and 3 feet.
- Check: All sides are equal (equilateral), so it cannot be a right triangle.
The only right triangle among the provided scenarios is the **triangular bike path with lengths of 5 miles, 12 miles, and 13 miles**.