The perimeter of a parallelogram is 24 cm. It is known that one side is compared to the other;

The perimeter of a parallelogram is 24 cm. It is known that one side is compared to the other; 1) less by 6 cm; 2) 2 times more. Find the sides of the parallelogram

Given:

ABCE – parallelogram,

1) AB – BC = 6 centimeters,

2) AB = 2 * BC,

the perimeter of ABCE is 24 centimeters.

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

Solution:

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

1) Let the length of the BC side be x centimeters, then the length of the AB side = 6 + x centimeters. We know that the ABCE perimeter is 24 centimeters. Let’s make the equation:

P avce = AB + CE + BC + AE;

24 = 6 + x + 6 + x + x + x;

4 * x = 24 – 12;

4 * x = 12;

x = 12: 4;

x = 3 centimeters – the lengths of the sides BC and AE;

3 + 6 = 9 centimeters – the lengths of the sides AB and CE.

2) Let the length of the BC side be x centimeters, then the length of the AB side = 2 * x centimeters. We know that the ABCE perimeter is 24 centimeters. Let’s make the equation:

P avce = AB + CE + BC + AE;

24 = 2 * x + 2 * x + x + x;

6 * x = 24;

x = 24: 6;

x = 4 centimeters – the lengths of the sides BC and AE;

4 * 2 = 8 centimeters – the lengths of the sides AB and CE.

Answer: 1) 3 centimeters, 3 centimeters, 9 centimeters, 9 centimeters; 2) 4 centimeters, 4 centimeters, 8 centimeters, 8 centimeters.