Using the Converse of the Pythagorean Theorem, explain whether a triangle with sides 15, 10, and 12 is a right triangle.(1 point) Responses No, because 244 is not equal to 225. No, because 244 is not equal to 225. No, because 325 is not equal to 144. No, because 325 is not equal to 144. No, because 369 is not equal to 100. No, because 369 is not equal to 100. No, because 22 is not equal to 15. No, because 22 is not equal to 15.
No, because 225 is not equal to 244.
The Converse of the Pythagorean Theorem states that if the sum of the squares of the two shorter sides of a triangle is equal to the square of the longest side, then the triangle is a right triangle.
In this case, the sum of the squares of 10 and 12 is equal to 100 + 144 = 244. However, the square of the longest side, which is 15, is equal to 225.
Since 244 is not equal to 225, the Converse of the Pythagorean Theorem tells us that this triangle is not a right triangle.
that is not an answer
No, using the Converse of the Pythagorean Theorem, a triangle with sides 15, 10, and 12 is not a right triangle because the sum of the squares of the two shorter sides (10 and 12) is not equal to the square of the longest side (15).
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 sum of the squares of the lengths of the two shorter sides is equal to the square of the length of the longest side.
In this case, we have the side lengths 15, 10, and 12. To use the Converse of the Pythagorean Theorem, we square each side length:
15^2 = 225
10^2 = 100
12^2 = 144
Now, we check if the sum of the squares of the two shorter sides (100 + 144 = 244) is equal to the square of the longest side (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.