To determine if a triangle with sides 15, 10, and 12 is a right triangle using the Converse of the Pythagorean Theorem, we first need to identify the longest side, which is 15. According to the 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 calculate:
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The square of the longest side (15): \[ 15^2 = 225 \]
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The squares of the other two sides (10 and 12): \[ 10^2 = 100 \] \[ 12^2 = 144 \]
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Now, add the squares of the two shorter sides: \[ 100 + 144 = 244 \]
Now we compare:
- Compare \(15^2\) (which is 225) to \(10^2 + 12^2\) (which is 244): \[ 225 \neq 244 \]
Since the square of the longest side (225) is not equal to the sum of the squares of the other two sides (244), we conclude that the triangle is not a right triangle.
The correct response is: No, because 244 is not equal to 225.