Question

question 4 of 10
suppose a triangle has sides 3, 4, and 5. 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

The Pythagorean theorem states that for a right triangle with side lengths \(a\), \(b\) (legs) and \(c\) (hypotenuse, the longest side), \(a^{2}+b^{2}=c^{2}\).

Step2: Identify the longest side

In the triangle with sides 3, 4, 5, the longest side is 5. So we check if \(3^{2}+4^{2}=5^{2}\).

Step3: Calculate each term

Calculate \(3^{2}=9\), \(4^{2} = 16\), and \(5^{2}=25\). Then, \(3^{2}+4^{2}=9 + 16=25\), and \(5^{2}=25\). So \(3^{2}+4^{2}=5^{2}\).

Answer:

C. The triangle in question is a right triangle.