Answer:
Given the statement: BE = 2x + 6 units and ED = 5x - 12 units.
By properties of parallelogram:
The parallelogram bisects each other at E.
You can see the diagram of parallelogram as shown below.
Therefore;
[tex]BE =ED[/tex] .....[1]
Substitute the given values we have;
[tex]2x+6 = 5x-12[/tex]
Add 12 both sides we get;
[tex]2x+18= 5x[/tex]
Subtract 2x from both sides we have;
[tex]18= 3x[/tex]
Divide 3 both sides we get;
x = 6.
BE = 2x+6 = 2(6)+6 = 12 +6 = 18 units
We have to find the value of BD:
BD = BE+ED
from [1] we have;
[tex]BD = 2BE[/tex]
[tex]BD = 2 \cdot 18 = 36 units[/tex]
Therefore, the value of BD is, 36 units.
