Using the Converse of the Pythagorean Theorem, explain whether a triangle with sides 15, 10, and 12 is a right triangle. (1 point) • No, because 369 is not equal to 100. • No, because 325 is not equal to 144. • No, because 244 is not equal to 225. • No, because 22 is not equal to 15.
No, because 325 is not equal to 144.
To determine whether a triangle with sides 15, 10, and 12 is a right triangle, we can apply the Converse of the Pythagorean Theorem. The theorem states that if the square of the longest side in 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 check if the given triangle is a right triangle, we need to calculate the sum of the squares of the other two sides: 10^2 + 12^2 = 100 + 144 = 244.
Since the square of the longest side, 15^2 (225), is not equal to the sum of the squares of the other two sides, 244, we can conclude that the triangle with sides 15, 10, and 12 is not a right triangle. Therefore, the correct answer is: No, because 244 is not equal to 225.
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 other two sides.
To apply the converse of the Pythagorean Theorem, we need to check if the square of the length of the longest side is equal to the sum of the squares of the other two sides.
So, let's calculate the values:
15^2 = 225
10^2 = 100
12^2 = 144
Now, let's check whether any of these values are equal to the sum of the squares of the other two sides:
225 is not equal to 100 + 144 = 244
100 is not equal to 225 + 144 = 369
144 is not equal to 225 + 100 = 325
Since none of these values are equal, we can conclude that the triangle with sides 15, 10, and 12 is not a right triangle. Therefore, the correct answer is: No, because 244 is not equal to 225.