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

A triangle with sides measuring 3, 4, and 5 fits the criteria for a right triangle due to the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

In this case, the length of the longest side is 5. According to the theorem, we check if:

[

3^2 + 4^2 = 5^2

]

Calculating the squares:

[

9 + 16 = 25

]

Since both sides of the equation are equal (25 = 25), this confirms that the triangle with sides of 3, 4, and 5 is indeed a right triangle.

In contrast, an equilateral triangle has all three sides equal, which is not the case here. An isosceles triangle features at least two sides of equal length, which also does not apply. Lastly, while an acute triangle has all angles less than 90 degrees, the triangle in question contains a right angle, thus ruling this out as well. This further solidifies that the correct classification of the triangle with sides 3,