The parallelogram has a perimeter of 70. The smaller side is 16. Find the larger side of the parallelogram.

A parallelogram is a quadrangle in which opposite sides are equal and lie on parallel lines:

AB = CD = 16 cm;

BC = AD.

The perimeter of a parallelogram is the sum of all sides of the parallelogram:

P = AB + BC + CD + AD.

In order to find the length of its larger side, we find the sum of its smaller sides:

AB + CD = 16 + 16 = 32cm.

In order to find the sum of two large torons, we find the difference between the perimeter and the sum of the two smaller ones:

BC + AD = P – (AB + CD);

BC + AD = 70 – 32 = 38 cm;

Now we divide this sum in half and get the length of the longer side:

BC = AD = 38/2 = 19 cm.

Answer: the length of the longer side of the parallelogram is 19 cm.