Question

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 22 is not equal to 15. No, because 22 is not equal to 15. 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.

Answer 1

To determine whether 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 lengths of the sides. We will denote them as \(a = 10\), \(b = 12\), and \(c = 15\) (the longest side). According to the theorem, for a triangle to be a right triangle, the following condition must hold:

\[ c^2 = a^2 + b^2 \]

Calculating each side:

1. \(c^2 = 15^2 = 225\)
2. \(a^2 + b^2 = 10^2 + 12^2 = 100 + 144 = 244\)

Now, we compare \(c^2\) with \(a^2 + b^2\):

• \(225 \neq 244\)

Since \(c^2\) is not equal to \(a^2 + b^2\), the triangle is not a right triangle.

Therefore, the correct response is: No, because 244 is not equal to 225.