In rectangle ABCD, the bisector of angle A is drawn before cutting with side BC at point K. Segment AK = 8 cm

| February 14, 2021 | education

In rectangle ABCD, the bisector of angle A is drawn before cutting with side BC at point K. Segment AK = 8 cm, the angle between the diagonals of the rectangle is 30 degrees. Find the sides and area of rectangle ABCD.

Since AK is the bisector of the angle ВAD, the triangle ABK is rectangular and isosceles, AB = ВK.

Then AK^2 = 2 * AB^2.

AB^2 = AK^2 / 2 = 64/2 = 32.

AB = ВK = 4 * √2 cm.

The AOB triangle is isosceles, since ОА = ОВ as half of the diagonals, and the angle AOB, by condition, is 30, then the angle ABO = (180 – 30) / 2 = 750.

In a right-angled triangle AВD, tg75 = BP / AВ.

AD= AB * tg75 = 4 * √2 * 3.73 = 21.1 cm.

Then Savsd = AB * AD = 4 * √2 * 21.1 = 84.4 * √2 cm2.

Answer: The sides of the rectangle are 4 * √2 cm, 21.1 cm, the area is 84.4 * √2 cm2.



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.