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.
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Identify the sides:
- \( a = 10 \)
- \( b = 12 \)
- \( c = 15 \) (longest side)
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Calculate the squares:
- \( a^2 = 10^2 = 100 \)
- \( b^2 = 12^2 = 144 \)
- \( c^2 = 15^2 = 225 \)
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Check the equation:
- We need to see if \( c^2 = a^2 + b^2 \)
- \( 225 = 100 + 144 \)
- \( 225 = 244 \) (this is incorrect; therefore, it indicates there was a mistake in calculating or matching.)
Now, let's examine the options provided regarding the relationships:
- The correct relationship according to the found values was \( 225 = 244 \) which does not hold. This means:
The answer to whether a triangle with sides 15, 10, and 12 is a right triangle is No, because 225 is not equal to 244.
Since the provided options do not directly match the values calculated, we find that the closest statement implying the relationships involve unequal values. None of the listed options directly state what we found, but the essence of the response confirms the triangle is not a right triangle.
Thus, the right interpretation is "No, because 225 is not equal to 244."