Answer: Three sides of a right triangle are the lengths of its legs and the length of its hypotenuse.
To know that three given sides will create a right triangle, we can use 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 legs. Symbolically, if a, b, and c are the lengths of the sides of a right triangle, with c being the hypotenuse, then:
c^2 = a^2 + b^2
Therefore, if we are given the lengths of three sides, we can square the lengths of the legs, add them together, and then take the square root to find the length of the hypotenuse. We can then compare the squared length of the hypotenuse to the sum of the squares of the legs. If they are equal, the three sides form a right triangle. If the squared length of the hypotenuse is greater than the sum of the squares of the legs, the three sides form an obtuse triangle. If the squared length of the hypotenuse is less than the sum of the squares of the legs, the three sides form an acute triangle.
Explanation: