Question

in the pythagorean theorem ($a^{2}+b^{2}=c^{2}$), the term $c^{2}$ represents the square of the:
a. area of the triangle
b. shortest side of the triangle
c. longest side of the triangle (hypotenuse)
d. middle - length side of the triangle

Explanation:

In the Pythagorean Theorem \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the lengths of the two legs of a right - triangle, and \(c\) is the length of the hypotenuse. The hypotenuse is the longest side of a right - triangle.

• Option a: The area of a right - triangle is \(A=\frac{1}{2}ab\), not related to \(c^{2}\).
• Option b: The shortest side is one of \(a\) or \(b\) (assuming \(a

eq b\) and \(a,b < c\) in a non - isosceles right - triangle).

• Option d: In a non - isosceles right - triangle, if \(a

eq b\), one of \(a\) or \(b\) is the middle - length side, not \(c\).

Answer:

c. Longest side of the triangle (hypotenuse)