Final answer:
A triangle with side lengths of 7 in., 9 in., and 11 in. is not a right triangle according to the Pythagorean theorem because the sum of the squares of the two shorter sides (7² + 9² = 130) does not equal the square of the longest side (11² = 121).
Step-by-step explanation:
To determine whether a triangle with side lengths of 7 in., 9 in., and 11 in. is a right triangle, we should apply the Pythagorean theorem. This theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b): a² + b² = c².
Lets calculate: 7² + 9² = 49 + 81 = 130 and 11² = 121.
Comparing these values, it is clear that 130 is not equal to 121. Therefore, this triangle is not a right triangle because 7² + 9² is not equal to 11². So, the correct answer is B. no, because 7² + 9² is not equal to 11².