A,B,C,D, and E are collinear points AE=34, BD=16 and AB=BC=CD.

Question

What is the length of CE?

Answer 1

A ,B ,C ,D and E are collinear points

AE = 34, BD = 16

AB = BC = CD

Substitute CD = BC

BD = BC + CD =16

BD = BC + BC = 16

BD = 2BC =16

2BC = 16

Divide each side by 2

BC = 16 / 2

BC = 8

There fore AB = BC =CD =8

CE = CD + DE

Substitute CD = 8

CE = 8 + DE

Substitute AE = 34

AE = AD + DE =34

AD = AB + BC + CD

Substitute AB =BC = CD = 8

AD = 8 + 8 + 8

There fore AD =24

But AE = AD + DE

Substitute AE = 34 and AD = 24

34 = 24 + DE

DE + 24 = 34

Subtract 24 from each side

DE +24 -24 = 34 - 24

DE = 10

But CE = CD + DE

CE = 8 + 10

There fore CE = 18.