Answer:
EB=20, BC=8, AC=16
Step-by-step explanation:
The symbols indicate that:
AB=BC and AE=ED
EB and CD are parallels
AB=BC=8
AC= AB+BC
AC= 8+8
AC=16
To find EB we can use the Cosine Law
For the upper triangle x=∡EAB:
EB^2 = AB^2 + AE^2 -2*AB*AE*Cosx
AB*AE*Cosx= -(EB^2-AB^2 - AE^2)/2 (Part I)
For de big triangle:
DC^2= AC^2+AD^2 -2AC*AD*Cosx
Also:
AC=2*AB
AD=2*AE
DC^2= (2*AB)^2 + (2*AE)^2 -2(2*AB)(2*AE)*Cosx
DC^2= 4*AB^2 +4*AE^2- 8*AB*AE*Cosx
AB*AE*Cosx =-(DC^2-4*AB^2 -4*AE^2)/8 (Part II)
Part I= Part II
-(EB^2-AB^2 - AE^2)/2= -(DC^2-4*AB^2 -4*AE^2)/8
Extracting EB:
EB^2=DC^2/4
EB=DC/2
EB=40/2
EB=20
