The perimeter of the parallelogram is 24 cm, and one of the sides is a quarter of the other.

| February 26, 2021 | education

The perimeter of the parallelogram is 24 cm, and one of the sides is a quarter of the other. What are the lengths of the sides of the parallelogram and how much of the perimeter does each of them make up?

1. Let’s denote the length of the longer side of the parallelogram by the index “a”, the length of the smaller side by the index “b”.

2. Let’s compose two equations:

(1) a = 4b;

(2) 2a + 2b = 24; a + b = 12;

3. Substitute the value a = 4b into the second equation:

4b + b = 12;

5c = 12;

h = 2.4 cm.

a = 2.4 x 4 = 9.6 cm.

4. We calculate what part is the smaller side of the parallelogram in relation to the perimeter:

2.4: 24 = 1/10.

5. We calculate what part is the large side of the parallelogram in relation to the perimeter:

9.6: 24 = 4/10.

Answer: the smaller side of the parallelogram is 2.4 cm and is 1/10 of the perimeter, the larger side of the parallelogram is 9.6 cm and is 4/10 of the perimeter.



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