The sides of a triangle have lengths 3, 4, and 6. What kind of triangle is it?acuterightobtuseSubmit

To determine the type of triangle, we can use the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. We can test this by squaring all the sides:

3^2 = 9 4^2 = 16 6^2 = 36

If it's a right triangle, then 6^2 should be equal to 3^2 + 4^2.

36 is not equal to 9 + 16 (which is 25), so it's not a right triangle.

If the square of the longest side is less than the sum of the squares of the other two sides, then the triangle is acute. If the square of the longest side is greater than the sum of the squares of the other two sides, then the triangle is obtuse.

In this case, 36 is greater than 25, so the triangle is obtuse.