The bisector of angle A of the parallelogram ABCD divides the side of CD in a ratio of 1: 3 counting from

| August 3, 2021 | education

The bisector of angle A of the parallelogram ABCD divides the side of CD in a ratio of 1: 3 counting from the top of angle C. Find the sides if the perimeter is 84 centimeters.

Let the bisector intersect with the side CD at the point K. Then the segment CK will be denoted by x cm, and KD by 3 * x cm.

The bisector of a parallelogram cuts off an isosceles triangle. Therefore, AD = KD = 3 * x cm.

The perimeter of a parallelogram with sides a and b is calculated by the formula:

Ppar-ma = 2 * (a + b).

We have one side equal to 3 * x cm, and the other – x + 3 * x = 4 * x cm. Substitute them into the perimeter formula and find x:

2 * (3 * x + 4 * x) = 84;

7 * x = 42;

x = 6 cm.

Then the sides of the parallelogram are equal:

3 * x = 3 * 6 = 18 cm;

4 * x = 4 * 6 = 24 cm;

Answer: the sides of the parallelogram are 18 cm and 24 cm.



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