Final answer:
Using the Pythagorean theorem, the sum of the squares of the two shorter sides (16 + 25 = 41) of the triangle does not equal the square of the longest side (49), thus the triangle is not a right triangle.
Step-by-step explanation:
To determine if a triangle with side lengths of 4 inches, 5 inches, and 7 inches is a right triangle, we can use the Pythagorean theorem. The theorem states that for a right triangle, the square of the length of the hypotenuse (the longest side of the triangle) is equal to the sum of the squares of the lengths of the other two sides.
Using the given side lengths, let's check if a² + b² = c², where a and b are the shorter sides (4 inches and 5 inches) and c is the longest side (7 inches).
a² = 4² = 16
b² = 5² = 25
c² = 7² = 49
Therefore, a² + b² = 16 + 25 = 41, which is not equal to c² (49). Hence, the triangle with sides 4 inches, 5 inches, and 7 inches is not a right triangle.