Question

Using the converse of the Pythagorean theorem explain whether a triangle with sides 15,10, and 12 is a right triangle.

Answer 1

[AI-generated answer — Bot GPT 3.5]

To determine whether a triangle with sides 15, 10, and 12 is a right triangle, we can use the converse of the Pythagorean theorem, which states:

"If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides, then the triangle is a right triangle."

In this case, the longest side is 15. So, if we can prove that the square of 15 is equal to the sum of the squares of 10 and 12, then the triangle is a right triangle.

Let's calculate the squares of the sides:
15^2 = 225
10^2 = 100
12^2 = 144

Now, let's check if the sum of the squares of the other two sides is equal to the square of the longest side:
100 + 144 = 244

The sum of the squares of 10 and 12 is 244, which is not equal to the square of 15 (225).

Since the sum of the squares of the two shorter sides is not equal to the square of the longest side, the triangle with sides 15, 10, and 12 is not a right triangle based on the converse of the Pythagorean theorem.