One of the sides of the parallelogram is 4 times larger than the other, its perimeter is 30 cm. which is the side of the parallelogram.
It is known that the perimeter (P) of a parallelogram is equal to the sum of the lengths of all its sides. Since the opposite sides of the parallelogram are pairwise equal, we can write that P = a + a + b + b = 2a + 2b, where a and b are the sides of the parallelogram.
Let x cm be the length of one side of the parallelogram, then 4x cm is the length of the second side. Then the perimeter of the parallelogram will be: 2 * x + 2 * 4x = 2x + 8x = 10x (cm).
By the condition of the problem, the perimeter of a given parallelogram is 30 cm, which means that we can write the following equality:
10x = 30.
Let’s solve the composed equation:
10x = 30,
x = 30: 10,
x = 3.
This means that one of the sides of the parallelogram is 3 cm, and the other side is 4x = 4 * 3 = 12 cm.
Answer: the sides of the parallelogram are 4 and 12 cm.
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