Triangle ABC has side lengths 7, 24, and 25. Do the side lengths form a Pythagorean triple?
test if 7^2 + 24^2 = 25^2
To determine if the side lengths of a triangle form a Pythagorean triple, we can apply the Pythagorean theorem. The theorem states that for a right-angled 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, the side lengths are 7, 24, and 25. So if the square of the longest side (25^2 = 625) is equal to the sum of the squares of the other two sides (7^2 + 24^2 = 49 + 576 = 625), then the side lengths form a Pythagorean triple.
In this case, since 625 is equal to 625, the side lengths 7, 24, and 25 do form a Pythagorean triple.