The two sides of the parallelogram are 1:19 apart and the perimeter is 80. Find the larger side of the parallelogram.

Let us denote the smaller side of the parallelogram by the letter X, then, in order to meet the condition of the problem, the larger side must be 19 x X. The perimeter is equal to the sum of the lengths of the sides. Let’s compose and solve the equation:
(19 x X + X) x 2 = 80;
(20 x X) x 2 = 80;
40 x X = 80;
X = 2.
We found the smaller side. The larger side will be equal to:
19 x 2 = 38.
Answer: The long side of the parallelogram is 38.