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 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, which is 15. According to the theorem, a triangle is a right triangle if the square of the longest side is equal to the sum of the squares of the other two sides.

Let's calculate:

1. The square of the longest side (15):
\[
15^2 = 225
\]

2. The squares of the other two sides (10 and 12):
\[
10^2 = 100
\]
\[
12^2 = 144
\]

3. Now, add the squares of the two shorter sides:
\[
100 + 144 = 244
\]

Now we compare:
- Compare \(15^2\) (which is 225) to \(10^2 + 12^2\) (which is 244):
\[
225 \neq 244
\]

Since the square of the longest side (225) is not equal to the sum of the squares of the other two sides (244), we conclude that the triangle is not a right triangle.

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