The perimeter of a parallelogram is 82. One side of a parallelogram is 29 larger than the other.

The perimeter of a parallelogram is 82. One side of a parallelogram is 29 larger than the other. Find the smaller side of the parallelogram.  

The perimeter of a parallelogram is the sum of all its sides. It is found by the formula: P = 2 (AB + BC).

Knowing that BC = AB + 29, we get P = 2 * (AB + AB + 29).

P = 2 * (2 * AB + 29);
P = 4 * AB + 58.

Knowing that the perimeter of the parallelogram ABCD is 82, we get:

4 * AB + 58 = 82;
4 * AB = 82 – 58;
4 * AB = 24;
AB = 24: 4;
AB = 6.

Answer: 6.