Final answer:
The length of each side of the rhombus can be found by using the Pythagorean theorem on the right-angled triangles formed by half of each diagonal. After calculation, the length of each side is found to be 13 cm, which is not listed in the given options.
Step-by-step explanation:
The question requires us to find the length of a side of a rhombus when the lengths of its diagonals are given. We can utilize the Pythagorean theorem to solve this problem because the diagonals of a rhombus bisect each other at right angles, thus forming four right-angled triangles.
Since the diagonals are 10 cm and 24 cm, each half of the diagonals will be 5 cm and 12 cm. So, for each right triangle formed by the halves of the diagonals, we have sides (half of diagonals) 5 cm and 12 cm, and we want to find the hypotenuse (which is a side of the rhombus).
The Pythagorean theorem states that a2 + b2 = c2, where a and b are the legs of the right triangle, and c is the hypotenuse. We calculate:
52 + 122 = 25 + 144 = 169
Taking the square root of 169, we get c = 13 cm. Therefore, the length of each side of the rhombus is 13 cm, which is not one of the options provided in the question. It appears there might be a mistake in the options given.