Question

In parallelogram ABCD , diagonals AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E, BE=2x2−x , and DE=x2+6 . What is BD ?

Answer 1

Refer to the diagram shown below.
BE = 2x² - x
DE = x² + 6

The intersecting diagonals bisect one another.
Therefore BE = DE, so that
2x² - x = x² + 6
x² - x - 6 = 0
Factorize.
(x + 2)(x - 3) = 0
x = -2, or x = 3.

When x = -2,
BE = 2(-2)² - (-2) = 10
DE = (-2)² + 6 = 10
Therefore BD = 20

When x = 3;
BE = 2(3²) - 3 = 15
DE = 3² + 6 = 15
Therefore BD = 30

Answer: Either 20 or 30.