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

A triangle with sides of lengths 3, 4, and 5 forms a special type of triangle known as a right triangle. This can be determined using 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 lengths of the other two sides.

In this case, we identify the longest side as 5. We then calculate:

• The square of 5: (5^2 = 25)

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

Since the sum of the squares of the two shorter sides (9 + 16 = 25) equals the square of the longest side (25), the triangle conforms to the Pythagorean theorem, which verifies that it is a right triangle.

Understanding the characteristics of the triangle is essential. A scalene triangle has all sides of different lengths, an isosceles triangle has two sides of equal length, and an equilateral triangle has all three sides equal. However, for the triangle with sides 3, 4, and