Jerry wants to create a right triangle with side lengths 3 millimeters, 5 millimeters, and 7 millimeters. Is this possible? Why or why not? No, because \( 3+5 \) is greater than 7 . No, because \( 3^{2}+5^{2} \) is not equal to \( 7^{2} \). Yes, because \( 3+5 \) is greater than 7 . Yes, because \( 3^{2}+5^{2} \) is equal to \( 7^{2} \).

Did you know that the Pythagorean Theorem is a game-changer when it comes to identifying right triangles? It 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 other two sides. For Jerry's situation, \( 3^2 + 5^2 = 9 + 25 = 34 \) and \( 7^2 = 49 \), so no right triangle can be formed. When testing for the possibility of forming a triangle, the triangle inequality theorem comes into play. It states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side. Here, \( 3 + 5 = 8 \), which is greater than 7, but \( 3 + 7 = 10 \) is greater than 5, and \( 5 + 7 = 12 \) is also greater than 3, so while it cannot form a right triangle, it technically can still form a triangle. Quite the twist!