Final answer:
Using the Pythagorean theorem, we find that triangle 1 has an unknown side of 5 cm, while triangle 2's unknown side does not equal 5 cm. Therefore, they will not fit together exactly along their unknown edges.
Step-by-step explanation:
To determine whether triangle 1 and triangle 2 will fit together along their unknown edges, we can apply the Pythagorean theorem. For a right-angled triangle, the theorem states that the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b), which can be written as c = √(a² + b²). In triangle 1, the lengths given are 3 cm, 4 cm, and x cm, which suggests the Pythagorean theorem as: x² = 3² + 4² = 9 + 16 = 25. Therefore, x = √25 = 5 cm. Triangle 2 has lengths of 13 cm, 12 cm, and y cm. Using the theorem again: y² = 13² + 12² = 169 + 144 = 313. Since the square root of 313 is not an integer, y is not equal to 5 cm, and consequently, triangle 1 and triangle 2 will not fit together exactly along the unknown edge since x ≠ y.