B is the midpoint of AC and D is the

Adela Brown

Adela Brown

Answered question

2022-01-09

B is the midpoint of AC and D is the midpoint of CE. Solve for x, given BD=3x+5 and AE =4x+20

Answer & Explanation

braodagxj

braodagxj

Beginner2022-01-10Added 38 answers

If B is the midpoint of AC, then AB=BC. If D is the midpoint of CE, then CD+DE
By the Segment Additional Postulate, AE=AB+BC+CD+DE. Since AB=BC and CD=DE, then AE=2BC+2CD=2(BC+CD). By the Segment Addition Postulate, BC+CD=BD so AE=2BD
It is given that BD=3x+5 ad AE=4x+20. Therefore:
AE=2BD
Substitute 4x+20=2(3x+5)
4x+20=6x+10
20=2x+10
10=2x
5=x

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