Using the Converse of the Pythagorean Theorem, explain whether a triangle with sides 15, 10, and 12 is a right triangle.
A: No, because 325 is not equal to 144.
B: No, because 22 is not equal to 15.
C: No, because 244 is not equal to 225.
D: No, because 369 is not equal to 100.
The correct answer is D: No, because 369 is not equal to 100.
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MathematicsGeometryPythagorean Theorem
Using the Converse of the Pythagorean Theorem, explain whether a triangle with sides 15, 10, and 12 is a right triangle.
A: No, because 325 is not equal to 144.
B: No, because 22 is not equal to 15.
C: No, because 244 is not equal to 225.
D: No, because 369 is not equal to 100.
To determine whether a triangle with sides 15, 10, and 12 is a right triangle, we can use the Converse of the Pythagorean Theorem.
The Converse of the Pythagorean Theorem states that if the square of the length of the longest side of a triangle is equal to the sum of the squares of the other two sides, then the triangle is a right triangle.
In this case, the longest side is 15.
To apply the Converse of the Pythagorean Theorem, we need to find the sum of the squares of the other two sides, which are 10 and 12.
1. Square the lengths of the other two sides:
10^2 = 100
12^2 = 144
2. Add the squares together:
100 + 144 = 244
Now, to check if the triangle is a right triangle, we compare the sum of the squares of the other two sides (244) to the square of the longest side (15^2 = 225).
Since 244 is not equal to 225, we can conclude that the triangle with sides 15, 10, and 12 is not a right triangle.
Therefore, the correct answer is C: No, because 244 is not equal to 225.