To determine if a triangle with sides 15, 10, and 12 is a right triangle using the Converse of the Pythagorean Theorem, we should first identify the longest side, which in this case is 15. The remaining sides are 10 and 12.
According to the Converse of the Pythagorean Theorem, a triangle is a right triangle if the square of the longest side is equal to the sum of the squares of the other two sides.
Let's perform the calculations:
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Square the lengths of the sides:
- Longest side (hypotenuse): \(15^2 = 225\)
- Other sides:
- \(10^2 = 100\)
- \(12^2 = 144\)
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Check the equality:
- Sum of the squares of the other two sides: \(100 + 144 = 244\)
Now we compare:
- \(15^2 (225)\) to \(10^2 + 12^2 (244)\).
Since \(225\) is not equal to \(244\), the triangle with sides 15, 10, and 12 is not a right triangle.
Therefore, the correct response from the options provided is: No, because 244 is not equal to 225.