Final answer:
The length of the hypotenuse of a right triangle with an area of 30 cm2 and a perimeter of 30 cm cannot be uniquely determined without more information. However, a common Pythagorean triple that fits the given conditions is 5, 12, and 13, thus the hypotenuse would be 13 cm.
Step-by-step explanation:
To find the length of the hypotenuse of a right triangle when the area and perimeter are known, we must recall two key formulas. The area (A) of a right triangle is calculated using the formula A = 1/2 × base × height, and the Pythagorean theorem relates the legs (a and b) of a right triangle to its hypotenuse (c) using a² + b² = c², which can be rewritten as c = √(a² + b²). It is given that the area is 30 cm² and the perimeter is 30 cm. Unfortunately, without having either the individual leg lengths or some other relevant piece of information, we cannot uniquely determine the length of the hypotenuse. The Hypotenuse of a Pythagorean triple of 5, 12, and 13 will indeed have the same perimeter and area, where the answer would be 13 cm.