In parallelogram ABCD, the height lowered to the side of CD divides it in half and forms an angle of 30 degrees

| September 2, 2021 | education

In parallelogram ABCD, the height lowered to the side of CD divides it in half and forms an angle of 30 degrees with side BC, AB = 26 cm. Find the perimeter of the parallelogram.

It is known:

Parallelogram ABCD;
The height BK, lowered to the CD side, divides it in half;
Angle CBK = 30 °;
AB = 26 cm.
Find the perimeter of the parallelogram.

1) AB = CD = 26 cm;

CK = 1/2 * CD = 1/2 * 26 cm = 13 cm;

2) Consider a triangle СBK with a right angle K.

sin B = CK / BC;

BC = CK / sin B;

Substitute the known values and calculate the side of the ВС parallelogram.

BC = 13 / sin 30 = 13 / (1/2) = 13 * 2/1 = 13 * 2 = 26 cm;

3) Find the perimeter of the parallelogram.

P = 2 * (a + b) = 2 * (26 cm + 26 cm) = 2 * 52 cm = 2 * 50 cm + 2 * 2 cm = 100 cm + 4 cm = 104 cm.

Answer: P = 104 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.