# In a parallelogram, the ratio of adjacent sides is 2, and its perimeter is 24 cm. What is the longest side of the parallelogram?

October 11, 2021 | education

| A parallelogram is a quadrangle in which opposite sides are pairwise parallel and equal to each other.

If the ratio of the adjacent sides of the parallelogram is 2, then:

AB / BC = 2;

AB = 2 · BC.

Since in a parallelogram the opposite sides are equal, the sum of its adjacent sides is equal to its semi-perimeter:

AB + BC = P / 2;

For the convenience of the calculation, we express:

BC = x;

AB = 2 BC = 2x;

x + 2x = 24/2;

3x = 12;

x = 12/3 = 4;

BC = 4 cm;

AB = 4 ∙ 2 = 8 cm.

Answer: the length of the longer side of the parallelogram is 8 cm.

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