In the parallelogram ABCD AB = 6, AD = 8, AC = 2√13. find BD.

univerkov | May 7, 2021 | education

Since the quadrilateral ABCD is a parallelogram, the sum of the squares of the lengths of its diagonals is equal to twice the sum of the squares of the lengths of its sides.

AC ^ 2 + BD ^ 2 = 2 * (AB ^ 2 + AD ^ 2).

BD ^ 2 = 2 * (AB ^ 2 + AD ^ 2) – AC ^ 2 = 2 * (36 + 64) – 4 * 13 = 200 – 52 = 148

ВD = √148 = 2 * √37 cm.

Answer: The length of the second diagonal is 2 * √37 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.