Question

suppose a triangle has sides 3, 4, and 6. which of the following must be true?
a. the triangle in question may or may not be a right triangle.
b. the triangle in question is not a right triangle.
c. the triangle in question is a right triangle.

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with sides \(a\), \(b\) (legs) and \(c\) (hypotenuse), \(a^{2}+b^{2}=c^{2}\).

Step2: Identify the sides

Let \(a = 3\), \(b = 4\), \(c = 6\) (where \(c\) is the longest side).

Step3: Calculate \(a^{2}+b^{2}\) and \(c^{2}\)

\(a^{2}+b^{2}=3^{2}+4^{2}=9 + 16=25\), and \(c^{2}=6^{2}=36\).

Step4: Compare results

Since \(25
eq36\), i.e., \(a^{2}+b^{2}
eq c^{2}\), the triangle is not a right - triangle.

Answer:

B. The triangle in question is not a right triangle.