Question

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

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

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 244 is not equal to 225.

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 lengths of the sides and designate the longest side.

1. Identify the sides:
- The sides are 15, 10, and 12.
- The longest side is 15.

2. Apply the Converse of the Pythagorean Theorem:
A triangle is a right triangle if the square of the length of the longest side is equal to the sum of the squares of the lengths of the other two sides.

So, we check if:
\[
15^2 = 10^2 + 12^2
\]

3. Calculate the squares:
- \(15^2 = 225\)
- \(10^2 = 100\)
- \(12^2 = 144\)

4. Add the squares of the shorter sides:
\[
10^2 + 12^2 = 100 + 144 = 244
\]

5. Compare:
\[
15^2 (225) \neq 10^2 + 12^2 (244)
\]

Since \(225\) is not equal to \(244\), we conclude that the triangle with sides 15, 10, and 12 is not a right triangle.

Thus, the correct reasoning is:
**No, because 244 is not equal to 225.**