Final answer:
Without additional information confirming that the triangle with sides of 25 cm and 30 cm is a right triangle, the length of the third side cannot be determined using the Pythagorean theorem.
Step-by-step explanation:
The question asks to find the length of the third side of a triangle using the Pythagorean theorem. First, we need to confirm if the triangle is a right triangle since the Pythagorean theorem is only applicable to right triangles. In a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. If we have two sides measuring 25 cm and 30 cm, and the area is 300 cm2, these cannot form a right triangle because the area calculation (1/2 base × height) would mean that one of these sides should be the height and the other the base, giving an area not equal to the given 300 cm2 when the formula is applied. Therefore, without additional information, the third side length cannot be determined using the Pythagorean theorem.