Given a triangle with side lengths $3$, $4$, and $5$, which best describes the triangle?

• A. It is an isosceles triangle because two sides are equal.
• B. It is an equilateral triangle because all sides are equal.
• C. It is a right triangle because $3^2+4^2=5^2$.
• D. It is an obtuse triangle because one angle is greater than $90°$.

Answer: (C)

Verified step by step guidance

1. Identify the side lengths of the triangle: 3, 4, and 5.
2. Recall the Pythagorean theorem, which states that in a right triangle, the square of the longest side (hypotenuse) equals the sum of the squares of the other two sides: \(a^2 + b^2 = c^2\).
3. Calculate the squares of the sides: \$3^2 = 9\(, \)4^2 = 16\(, and \)5^2 = 25$.
4. Check if the sum of the squares of the two shorter sides equals the square of the longest side: \$9 + 16 = 25$.
5. Since the equation holds true, conclude that the triangle is a right triangle.