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

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

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

Answer: (C)

A triangle with sides of length 3, 4, and 5 can be classified as a right triangle due to the relationship between the lengths of the sides. According to the Pythagorean theorem, for a triangle to be a right triangle, the square of the length of the longest side must equal the sum of the squares of the lengths of the other two sides. In this case, the longest side is 5. We can check: - The square of the longest side: \(5^2 = 25\) - The sum of the squares of the other two sides: \(3^2 + 4^2 = 9 + 16 = 25\) Since both values are equal (25 = 25), this confirms that the triangle indeed has a right angle. In addition, each side of this triangle has a different length, confirming it is not equilateral (which requires all sides to be equal) or isosceles (which requires at least two sides to be of equal length). Therefore, the classification as a right triangle is accurate.

A triangle with sides of length 3, 4, and 5 can be classified as a right triangle due to the relationship between the lengths of the sides. According to the Pythagorean theorem, for a triangle to be a right triangle, the square of the length of the longest side must equal the sum of the squares of the lengths of the other two sides.

In this case, the longest side is 5. We can check:

• The square of the longest side: (5^2 = 25)

• The sum of the squares of the other two sides: (3^2 + 4^2 = 9 + 16 = 25)

Since both values are equal (25 = 25), this confirms that the triangle indeed has a right angle.

In addition, each side of this triangle has a different length, confirming it is not equilateral (which requires all sides to be equal) or isosceles (which requires at least two sides to be of equal length). Therefore, the classification as a right triangle is accurate.