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

To determine if a triangle with side lengths 3, 4, and 5 is a right triangle, we can apply 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, which is 5. We then calculate the squares of the side lengths:

• The square of the hypotenuse: (5^2 = 25)
• The square of the first side: (3^2 = 9)
• The square of the second side: (4^2 = 16)

Next, we add the squares of the two shorter sides:

[ 3^2 + 4^2 = 9 + 16 = 25 ]

Now we can compare the results from the Pythagorean theorem:

[ 5^2 = 3^2 + 4^2 ] [ 25 = 25 ]

Since the equality holds true, it confirms that the triangle with sides 3, 4, and 5 satisfies the Pythagorean