A triangle has sides with lengths of 9 yards, 12 yards, and 15 yards. Is it a right triangle? yes no Submit

**Yes**, the triangle with sides measuring 9 yards, 12 yards, and 15 yards is a right triangle. ### Here's why: To determine if a triangle is a right triangle, you can use the **Pythagorean Theorem**, which states that in a right-angled triangle: \[ \text{(Shortest side)}^2 + \text{(Middle side)}^2 = \text{(Longest side)}^2 \] Let's apply this to your triangle: 1. **Identify the longest side (hypotenuse):** - The lengths are 9 yards, 12 yards, and 15 yards. - The longest side is **15 yards**. 2. **Apply the Pythagorean Theorem:** \[ 9^2 + 12^2 = 15^2 \] \[ 81 + 144 = 225 \] \[ 225 = 225 \] 3. **Conclusion:** - Since both sides of the equation are equal, the triangle satisfies the Pythagorean Theorem. - Therefore, the triangle is indeed a **right triangle**. ### Summary: - **Sides:** 9 yards, 12 yards, 15 yards - **Longest side (hypotenuse):** 15 yards - **Calculation:** \( 9^2 + 12^2 = 225 \) and \( 15^2 = 225 \) - **Result:** \( 225 = 225 \) ✔️ So, the triangle is a right triangle.