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

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

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

Answer: (D)

A triangle with sides of lengths 3, 4, and 5 is classified as a right triangle because it satisfies the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, if we designate the longest side (5) as the hypotenuse, we can calculate the squares of the side lengths: - The square of 5 is \(5^2 = 25\). - The square of 4 is \(4^2 = 16\). - The square of 3 is \(3^2 = 9\). When we add the squares of the lengths of the other two sides, we find: \[16 + 9 = 25\] Since the sum of the squares of the two shorter sides (16 + 9) equals the square of the longest side (25), it confirms that the triangle is indeed a right triangle. To further contextualize this, an equilateral triangle would have all three sides equal, which does not apply here. An isosceles triangle requires at least two sides to be of equal

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

In this case, if we designate the longest side (5) as the hypotenuse, we can calculate the squares of the side lengths:

• The square of 5 is (5^2 = 25).

• The square of 4 is (4^2 = 16).

• The square of 3 is (3^2 = 9).

When we add the squares of the lengths of the other two sides, we find:

[16 + 9 = 25]

Since the sum of the squares of the two shorter sides (16 + 9) equals the square of the longest side (25), it confirms that the triangle is indeed a right triangle.

To further contextualize this, an equilateral triangle would have all three sides equal, which does not apply here. An isosceles triangle requires at least two sides to be of equal