Using the Converse of the Pythagorean Theorem, explain whether a triangle with

Question

sides 15, 10, and 12 is a right triangle. (1 point)
No, because 325 is not equal to 144.
No, because 369 is not equal to 100.
No, because 22 is not equal to 15.
No, because 244 is not equal to 225.

Answer 1

To determine whether a triangle with sides 15, 10, and 12 is a right triangle using the Converse of the Pythagorean Theorem, we need to check if the square of the longest side is equal to the sum of the squares of the other two sides.

1. Identify the sides:

   • The longest side is 15 (let's call it \(c\)), and the other two sides are 10 and 12 (let's call them \(a\) and \(b\)).

2. According to the Pythagorean Theorem, for a triangle to be a right triangle, the following must hold: \[ c^2 = a^2 + b^2 \]

3. Calculate \(c^2\): \[ 15^2 = 225 \]

4. Calculate \(a^2 + b^2\): \[ 10^2 + 12^2 = 100 + 144 = 244 \]

5. Now, compare \(c^2\) and \(a^2 + b^2\): \[ 225 \neq 244 \]

Since \(15^2\) (which is 225) is not equal to \(10^2 + 12^2\) (which is 244), we conclude that the triangle with sides 15, 10, and 12 is not a right triangle.

Thus, the answer to the question is: No, because 244 is not equal to 225.