Hakirn wants to create a right triangle with side lengths 11 inches, 45 inches, and 46 inches. Is this possible? Why or why not? Yes, because \( 11+45 \) is not equal to 46 . Yes, because \( 11^{2}+45^{2} \) is not equal to \( 46^{2} \). No, because \( 11^{2}+45^{2} \) is greater than \( 46^{2} \). No, because \( 11+45 \) is greater than 46 .

To determine if a triangle can be a right triangle, we can use the Pythagorean theorem, which states that for a right triangle with legs \( a \) and \( b \) and hypotenuse \( c \), the equation \( a^2 + b^2 = c^2 \) holds true. In this case, we calculate \( 11^2 + 45^2 \) and compare it to \( 46^2 \). Surprisingly, \( 11^2 + 45^2 = 121 + 2025 = 2146 \) while \( 46^2 = 2116 \). Since \( 2146 \) is greater than \( 2116 \), this doesn’t satisfy the theorem, indicating that these side lengths cannot form a right triangle. Now, here’s a fun fact: The largest angle in a triangle is always opposite its longest side. In this case, \( 46 \) inches is the longest side (hypotenuse), meaning the angle opposite it should be the largest. However, because \( 11 \), \( 45 \), and \( 46 \) cannot satisfy the Pythagorean theorem, you won’t find any right angles here! It's almost like trying to fit a square peg in a round hole—sometimes even the longest side can lead you astray!