Question

Using the converse of the Pythagorean theorem explain wheather a triangle with sides 15, 10 , an 12 is a right triangle

Answer 1

The converse of the Pythagorean theorem states that if a triangle has side lengths \(a\), \(b\), and \(c\) (where \(c\) is the longest side), and if \(a^2 + b^2 = c^2\), then the triangle is a right triangle.

In this case, we have the side lengths 15, 10, and 12. First, we need to identify the longest side, which is 15. Therefore, we can assign:

- \(a = 10\)
- \(b = 12\)
- \(c = 15\)

Now, we will check whether \(a^2 + b^2 = c^2\):

1. Calculate \(a^2\):
\[
a^2 = 10^2 = 100
\]

2. Calculate \(b^2\):
\[
b^2 = 12^2 = 144
\]

3. Calculate \(c^2\):
\[
c^2 = 15^2 = 225
\]

Now, we check if \(a^2 + b^2 = c^2\):
\[
a^2 + b^2 = 100 + 144 = 244
\]

Since \(244 \neq 225\), it follows that \(a^2 + b^2 \neq c^2\).

Therefore, according to the converse of the Pythagorean theorem, a triangle with sides 15, 10, and 12 is **not** a right triangle.