To determine whether a triangle with sides 15, 10, and 12 is a right triangle using the Converse of the Pythagorean Theorem, we first identify the longest side, which is 15.
According to the Pythagorean Theorem, for a triangle to be a right triangle, the square of the longest side (hypotenuse) must be equal to the sum of the squares of the other two sides (the legs).
Let's calculate:
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The longest side squared: \( 15^2 = 225 \)
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The other two sides squared: \( 10^2 = 100 \) \( 12^2 = 144 \)
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Now, add the squares of the two shorter sides: \( 100 + 144 = 244 \)
Now we can use the Converse of the Pythagorean Theorem:
For the triangle to be a right triangle, we need: \( c^2 = a^2 + b^2 \) Where \( c \) is the longest side.
We find: \( 15^2 \) (225) should equal \( 10^2 + 12^2 \) (244).
Since: \( 225 \neq 244 \)
Thus, we conclude that the triangle is not a right triangle.
The correct response from the options you provided is: No, because 244 is not equal to 225.