Question

1. 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. longest side of the triangle (hypotenuse)
c. shortest side of the triangle
d. middle - length side of the triangle

Explanation:

In the Pythagorean Theorem \(a^{2}+b^{2}=c^{2}\), \(a\) 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 side opposite the right angle and is the longest side of a right - triangle. The formula relates the squares of the lengths of the sides of a right - triangle. Option A is incorrect because the area of a right - triangle is \(\frac{1}{2}ab\). Options C and D are incorrect as \(c\) is defined as the hypotenuse (longest side) in the Pythagorean Theorem.

Answer:

B. Longest side of the triangle (hypotenuse)