What does the variable c represent in the Pythagorean Theorem?

In the Pythagorean Theorem, which is expressed as ( a^2 + b^2 = c^2 ), the variable ( c ) specifically represents the length of the hypotenuse of a right triangle. The hypotenuse is the longest side of the triangle and is opposite the right angle.

Understanding the roles of the sides is crucial in applying the theorem correctly. The two other sides, represented by ( a ) and ( b ), are the legs of the triangle. The theorem provides a relationship among these three sides, demonstrating how the squares of the lengths of the legs add up to the square of the length of the hypotenuse.

The other options relate to properties of triangles but do not define ( c ) in the context of the Pythagorean theorem. For instance, the length of one of the shorter sides pertains to ( a ) or ( b ), while the area and perimeter describe different aspects of a triangle entirely and are not represented by ( c ). Thus, the correct focus on ( c ) as the length of the hypotenuse helps in understanding the fundamental application of the theorem in geometry.