In parallelogram ABCD, side AB is 5√2 and angle B is 135 degrees. Find the height of the parallelogram.

univerkov | May 26, 2021 | education

From the vertex B of the parallelogram, draw the height BH.

Determine the angles of a right-angled triangle ABH.

Angle ABM = ABC – HBC = 135 – 90 = 450.

Then the angle BАH = 180 – 90 – 45 = 450.

Then triangle ABH is rectangular and isosceles.

Determine the length of the leg BH.

AB ^ 2 = BH ^ 2 + AH ^ 2 = 2 * BH ^ 2.

BH ^ 2 = AB ^ 2/2 = (5 * √2) ^ 2/2 = 50/2 = 25.

BH = √25 = 5 cm.

Answer: The height of the parallelogram is 5 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.