Eighth grade T. T Converse of the Pythagorean theorem: is it a right triangle? Eaz A triangle has sides with lengths of 18 inches, 24 inches, and 31 inches. Is it a right triangle? yes no Submit

To determine whether a triangle with sides of **18 inches**, **24 inches**, and **31 inches** is a right triangle, we can use the **Converse of the Pythagorean Theorem**. ### **Converse of the Pythagorean Theorem** The converse states that **if the square of the longest side** (called the **hypotenuse**) **is equal to the sum of the squares of the other two sides**, then the triangle is a **right triangle**. ### **Steps to Determine if it's a Right Triangle** 1. **Identify the Longest Side:** - In this case, **31 inches** is the longest side. 2. **Apply the Pythagorean Theorem:** - Check if \( a^2 + b^2 = c^2 \), where \( c \) is the longest side. \[ 18^2 + 24^2 = 324 + 576 = 900 \] \[ 31^2 = 961 \] 3. **Compare the Results:** - \( 900 \) (sum of squares of the shorter sides) **does not equal** \( 961 \) (square of the longest side). ### **Conclusion** Since \( 18^2 + 24^2 \neq 31^2 \), the triangle **is not** a right triangle. **Answer:** No