Final answer:
The side lengths of 7, √56, and 2 do not form a right triangle because they do not satisfy the Pythagorean theorem, which is a requirement for the sides of a right triangle.
Step-by-step explanation:
To determine if the side lengths of 7, √56, and 2 form a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the two shorter sides (legs) must equal the square of the longest side (the hypotenuse). The formula is a² + b² = c², where c is the hypotenuse, and a and b are the legs of the triangle.
Let's check if these side lengths satisfy this condition. First, we calculate the square root of 56:
√56 = √(8 × 7) = √8 × √7 = 2√7
Now, check if the squares of 7 and 2 add up to the square of 2√7:
7² + 2² = 49 + 4 = 53
(2√7)² = 4 × 7 = 28
Since 53 is not equal to 28, the side lengths of 7, √56, and 2 do not form a right triangle.