One of the sides of the parallelogram is 3 times smaller than the other, and its perimeter is 72 cm. Find the sides of the parallelogram.
Let X centimeters be one of the sides of the parallelogram. Then the other side of the parallelogram is 3X centimeters (since it is 3 times larger). It is known that the perimeter of a parallelogram is 72 centimeters.
The perimeter is the sum of all sides of the parallelogram. From this statement we obtain the formula:
P = a + a + b + b = 2a + 2b = 2 * (a + b).
Where P is the perimeter; a and b are the sides of the parallelogram.
Let’s find the sides of this parallelogram:
72 = 2 * (X + 3X) = 2 * 4X;
4X = 72: 2;
4X = 36;
X = 36: 4;
X = 9.
Thus, one of the sides of the parallelogram is 9 centimeters.
Let’s find the other side of the parallelogram:
9 * 3 = 27 (centimeters) – the second side of the parallelogram.
Since in a parallelogram the two opposite sides are equal and parallel, in this parallelogram the sides are: 9 and 9; 27 and 27.
Answer: 9; nine; 27; 27.
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