Question

Given parallelogram ABCD, diagonals AC and BD intersect at point E. AE=2x, BE=y+10, CE=x+2 and DE=4y−8. Find the length of BD.

Answer 1

Okay, according with the identities of parallelograms we have: AE=CE and BE=DE.

Replacing we obtain:

AE=CE

2x=x+2

2x-x=2

x=2

BE=DE

y+10=4y−8

10+8=4y-y

18=3y

y=18/3

y=6

And considering that BD=BE+DE, we got:

BD=(y+10)+(4y-8)=(6+10)+(4*6-8)=(16)+(24-8)=16+16=32

So, finally we obtain that the length of BD is 32 units.