Using the Converse of the Pythagorean Theorem, explain whether a triangle with sides 15, 10, and 12 is a right triangle. (1 point)
O No, because 369 is not equal to 100.
O No, because 244 is not equal to 225.
O No, because 22 is not equal to 15.
O No, because 325 is not equal to 144.
O 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 Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
In this case, the longest side of the triangle is 15, so we can check if the sum of the squares of the other two sides (10 and 12) is equal to the square of 15.
Calculating the sum of the squares, we have:
10^2 + 12^2 = 100 + 144 = 244.
Since 244 is not equal to 15^2 (which is 225), we can conclude that the triangle with sides 15, 10, and 12 is not a right triangle.
Therefore, the correct option is: O No, because 244 is not equal to 225.
To determine if a triangle is a right triangle, we can use the converse of the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, we have a triangle with sides measuring 15, 10, and 12. To apply the converse of the Pythagorean theorem, we need to check if the square of the longest side (15) is equal to the sum of the squares of the other two sides (10 and 12).
Calculating the squares of the sides:
15 squared is equal to 15 x 15 = 225.
10 squared is equal to 10 x 10 = 100.
12 squared is equal to 12 x 12 = 144.
Now, we need to check if the sum of the squares of the other two sides (100 + 144) is equal to the square of the longest side (225).
100 + 144 = 244, which is not equal to 225.
Therefore, using the converse of the Pythagorean theorem, we can conclude that the given triangle with sides 15, 10, and 12 is not a right triangle.