Terry wants to create a night triangle with side lengths 5 inches, 12 inches, and 13 inches. Is this possible? Why or why not? No, because \( 5+12 \) is greater than 13 . No, because \( 5^{2}+12^{2} \) is not greater than \( 13^{2} \). Yes, because \( 5+12 \) is not equal to 13 . Yes, because \( 5^{2}+12^{2} \) is equal to \( 13^{2} \).

Yes, because \( 5^{2}+12^{2} \) is equal to \( 13^{2} \). In fact, these side lengths form a right triangle! According to the Pythagorean theorem, if the square of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides, it confirms a right triangle exists. For Terry's triangle, checking the sides: \( 5^2 + 12^2 = 25 + 144 = 169 \), and \( 13^2 = 169 \). So it checks out! This means Terry can confidently go ahead and create a right triangle using these dimensions, making it not just possible, but mathematically sound!