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 longest side, which will be considered the hypotenuse.
In this case, the sides are:
- a = 10
- b = 12
- c = 15 (the longest side)
According to the Pythagorean Theorem, \(c^2 = a^2 + b^2\) for a right triangle.
Now, we will compute:
- \(c^2 = 15^2 = 225\)
- \(a^2 + b^2 = 10^2 + 12^2 = 100 + 144 = 244\)
Now we see if \(c^2\) equals \(a^2 + b^2\):
- 225 is not equal to 244.
Since \(c^2 \neq a^2 + b^2\), we conclude that the triangle is not a right triangle.
The correct response is: No, because 244 is not equal to 225.