If a triangle has sides of lengths 3, 4, and 5, what type of triangle is it?

• A. Scalene
• B. Isosceles
• C. Equilateral
• D. Right

Answer: (D)

A triangle with sides of lengths 3, 4, and 5 is classified as a right triangle. This determination is based on the Pythagorean Theorem, which states that in a right triangle, the square of the length of the longest side (the hypotenuse) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the longest side is 5. We can verify whether it is a right triangle by calculating:

• (3^2 + 4^2 = 9 + 16 = 25)

• (5^2 = 25)

Since both sides of the equation are equal (25 = 25), it confirms that the triangle adheres to the Pythagorean Theorem, indicating that it contains a right angle. Consequently, the triangle formed by the sides of lengths 3, 4, and 5 is indeed a right triangle.