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

univerkov | March 5, 2021 | education

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

The bisector AK of the angle BAD cuts off at the lateral side AD an isosceles triangle ADK, in which DK = AD.

Let the length of the segment SK = X cm, then, by condition, DK = 3 * X cm.

Then AD = DK = 3 * X cm, CD = CK + DK = X + 3 * X = 4 * X cm.

Then the perimeter of the parallelogram is: (3 * X + 4 * X + 3 * X + 4 * X) = 84 cm.

14 * X = 84 cm.

X = 84/14 = 6 cm.

Then AB = CD = 4 * 6 = 24 cm, BC = AD = 3 * 6 = 18 cm.

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

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.