Final answer:
It is not possible to form a right triangle with lengths 2 inches, 4 inches, and 7 inches because the Pythagorean theorem's condition, 2² + 4² = 7², is not satisfied since 4 + 16 does not equal 49.
Step-by-step explanation:
To determine if a set of three lengths can form a right triangle, we use the Pythagorean theorem, which states that for a right triangle with legs a and b, and hypotenuse c, the relationship is given by: a² + b² = c². The theorem can also be expressed as: c = √a² + b². For the lengths given, 2 inches, 4 inches, and 7 inches, we can test this relationship.
When applying the theorem to the given lengths, we find:
- 2² + 4² = 4 + 16 = 20
- 7² = 49
Since 20 is not equal to 49, the equation 2² + 4² != 7² shows that these lengths do not satisfy the Pythagorean theorem and cannot form a right triangle.