The bisector of angle B into rectangle ABCD divides side AD into segments 2 and 6 cm long.

univerkov | August 16, 2021 | education

The bisector of angle B into rectangle ABCD divides side AD into segments 2 and 6 cm long. Find the perimeter of the rectangle.

Since ABCD is a rectangle, the bisector BM divides the right angle in half.

Then the angle ABM = 90/2 = 450.

The ABM triangle is rectangular, in which one of the acute angles is 45, then in the ABM triangle the lengths of the legs AB and AM are equal.

AB = AM = 2 cm.

Side length AD = AM + DM = 2 + 6 = 8 cm.

Since the opposite sides of the rectangle are equal, then Ravsd = 2 * (AB + AD) = 2 * (2 + 8) = 20 cm.

Answer: The perimeter of the rectangle is 20 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.