The perimeter of parallelogram ABCD is 80 cm, A = 30 °, and the perpendicular BH to line AD is 7.5 cm.
| April 28, 2021 | education
The perimeter of parallelogram ABCD is 80 cm, A = 30 °, and the perpendicular BH to line AD is 7.5 cm. Find the sides of the parallelogram.
Since, according to the condition, ВН is perpendicular to AD, then the ABН triangle is rectangular, in which the ВAН angle, by condition, is 30.
Then the ВН leg lies opposite the angle 30, which means it is equal to half the length of the hypotenuse.
BH = AB / 2. Then AB = 2 * BH = 2 * 7.5 = 15 cm.
In a parallelogram, the lengths of the opposite sides are equal. AB = CD = 15 cm. BC = AD.
The perimeter of the parallelogram is: Ravsd = 2 * (AB + BC) = 80.
AB + BC = 40.
BC = 40 – AB = 40 – 15 = 25 cm.
Answer: The sides of the parallelogram are 15 cm and 25 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.
