To determine whether the triangle with sides 15, 10, and 12 is a right triangle, we can use the Converse of the Pythagorean Theorem. The theorem states that if a triangle is a right triangle, then the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.
First, we identify the lengths of the sides:
- The longest side is 15.
- The other two sides are 10 and 12.
Next, we calculate the squares of the sides:
- \(15^2 = 225\)
- \(10^2 = 100\)
- \(12^2 = 144\)
Now, we check the Pythagorean Theorem: \[ 15^2 = 10^2 + 12^2 \] This simplifies to: \[ 225 = 100 + 144 \] Calculating the right side gives: \[ 100 + 144 = 244 \]
Since \(225 \neq 244\), it follows that the condition of the Converse of the Pythagorean Theorem is not satisfied. Therefore, the triangle with sides 15, 10, and 12 is not a right triangle.
The correct response is: No, because 244 is not equal to 225.