Question

using the converse of the pythagorean theorem, explain whether a triangle with sides 15, 10, and 12 is a right triangle. (1 point)
no, because 325 is not equal to 144.
no, because 244 is not equal to 225
no, because 369 is not equal to 100.
no, because 22 is not equal to 15.

Explanation:

Step1: Identify the longest side

The longest side of the triangle is \(15\).

Step2: Apply the Converse of the Pythagorean Theorem

The Converse of the Pythagorean Theorem states that if \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side of the triangle, then the triangle is a right - triangle. Let \(a = 10\), \(b=12\) and \(c = 15\).
Calculate \(a^{2}+b^{2}\):
\(a^{2}+b^{2}=10^{2}+12^{2}=100 + 144=244\)
Calculate \(c^{2}\):
\(c^{2}=15^{2}=225\)

Answer:

No, because \(244\) is not equal to \(225\) (the second option).