Question

AB=8 and CD =40 find EB ,BC and AC

Answer 1

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