The perimeter of a parallelogram is 112 cm, and its two sides are 5: 3. Find the sides of the parallelogram.

Given:

ABCE – parallelogram,

AB: BC = 5: 3,

the perimeter of ABCE is 112 centimeters.

Find the lengths of the sides of the parallelogram ABCE: AB, CE, BC, AE -?

Decision:

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 3x centimeters, then the length of the AB side = 5 * x centimeters. We know that the ABCE perimeter is 112 centimeters. Let’s make the equation:

P avce = AB + CE + BC + AE;

112 = 5 * x + 5 * x + 3 * x + 3 * x;

112 = x * (5 + 5 + 3 + 3)

16 * x = 112;

x = 112: 16;

x = 7 centimeters;

3 * 7 = 21 centimeters – the lengths of the sides BC and AE;

5 * 7 = 35 centimeters – the lengths of the sides AB and CE.

Answer: 21 centimeters; 21 centimeters; 35 centimeters; 35 centimeters.