The perimeter of the parallelogram is 19 cm. The quintupled first side is 0.7 cm longer than

The perimeter of the parallelogram is 19 cm. The quintupled first side is 0.7 cm longer than the quadrupled second side. Find the sides of the parallelogram.

The perimeter of a parallelogram is equal to the sum of the lengths of its four sides. Since in a parallelogram the opposite sides are equal, half of its perimeter is equal to the sum of the lengths of two adjacent sides, p / 2 = 19/2 = 9.5 (cm).

Let one side of the parallelogram be equal to x cm, then the second side is equal to (9.5 – x) cm. The quintuple first side is 5x cm, and the quadruple second side is 4 (9.5 – x) cm. By the condition of the problem, it is known that the quintuple the first side is larger than the quadrupled second side by (5x – 4 (9.5 – x)) cm or 0.7 cm. Let’s make an equation and solve it.

5x – 4 (9.5 – x) = 0.7;

5x – 38 + 4x = 0.7;

9x = 0.7 + 38;

9x = 38.7;

x = 38.7: 9;

x = 4.3 (cm) – first side;

9.5 – x = 9.5 – 4.3 = 5.2 (cm) – second side.

Answer. 4.3 cm; 5.2 cm.