Question

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 325 is not equal to 144. No, because 325 is not equal to 144. No, because 244 is not equal to 225. No, because 244 is not equal to 225. No, because 22 is not equal to 15. No, because 22 is not equal to 15. No, because 369 is not equal to 100.

Answer 1

To determine if a triangle with sides 15, 10, and 12 is a right triangle using the Converse of the Pythagorean Theorem, we first need to identify the longest side and then apply the theorem.

1. The longest side is 15. We will check if \(15^2 = 10^2 + 12^2\).

Calculating each term:

• \(15^2 = 225\)
• \(10^2 = 100\)
• \(12^2 = 144\)

Now add \(10^2\) and \(12^2\):

• \(100 + 144 = 244\)

Now, compare \(15^2\) with the sum of \(10^2\) and \(12^2\):

• \(225 \neq 244\)

Since \(15^2\) (which is 225) is not equal to \(10^2 + 12^2\) (which is 244), we conclude that the triangle is not a right triangle.

The correct response would be: No, because 225 is not equal to 244.