# One of the sides of the parallelogram is 4 times smaller than the other side.

**One of the sides of the parallelogram is 4 times smaller than the other side. Find the length of the longer side if the parallelogram perimeter is 50 cm.**

Given:

ABCE – parallelogram,

AB = 4 * BC,

the perimeter of ABCE is 50 centimeters.

Find the length of the larger side of the parallelogram AВСD, that is, AB -?

Solution:

Consider a parallelogram ABCE. Its opposite sides are equal to each other, then BC = AE, AB = CE.

Let the length of the BC side be x centimeters, then the length of the AB side = 4 * x centimeters. We know that the ABCE perimeter is 50 centimeters. Let’s make the equation:

P avce = AB + CE + BC + ADE

50 = 4 * x + 4 * x + x + x;

50 = x * (4 + 4 + 1 + 1);

10 * x = 50;

x = 50: 10;

x = 5 centimeters – the lengths of the sides BC and AE;

4 * 5 = 20 centimeters – the lengths of the sides AB and CE90.

Answer: 20 centimeters.