\[ \begin{array}{l} (40+42)^{2}=58^{2} \\ 82^{2}=3,364 \\ 6,724 \neq 3,364 \end{array} \] The triangle is not a right triangle. \[ \begin{array}{l} 42^{2}+40^{2}=58^{2} \\ 1,764+1,600 \stackrel{?}{=} 3,364 \\ 3,364=3,364 \end{array} \] The triangle is a right triangle. Which best describes the accuracy of their solutions? Holly is correct. Tamar is correct.

Holly and Tamar have provided reasoning based on the Pythagorean theorem, which states that in a right 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. This theorem was established in ancient Greece, and its applications can be seen in various fields, including construction, navigation, and physics. When determining whether a triangle is a right triangle, make sure to check and recheck your calculations for accuracy! Many mistakes can occur during squaring numbers or adding them up. In this case, Holly's assertion that \( (40 + 42)^2 \) leads to an inequality is incorrect because she miscalculated. Always double-check your numbers, especially when dealing with the relationships between sides in triangles!