Question

Given C is the midpoint of line AB, D is the midpoint of line AC, and E is the midpoint of line DC. If AE=16, what is DB?

Answer 1

DB = 32

Explanation:

Given :

⇒ C is the midpoint of the line AB

⇒ E is the midpoint of the line DC

⇒ AE = 16

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Understanding :

⇒ AC = BC = 1/2AB

⇒ AD = DC = 1/2AC = 1/4AB

⇒ DE = 1/2AD = 1/4AC = 1/8AB

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Finding AB :

⇒ AE = AD + DE

⇒ 16 = 1/4AB + 1/8AB

⇒ 3/8AB = 16

⇒ AB = 16 x 8 / 3

⇒ AB = 128/3

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Finding DB :

⇒ DB = DC + CB

⇒ DB = 1/4AB + 1/2AB

⇒ DB = 3/4AB

⇒ DB = 3/4 × 128/3

⇒ DB = 128/4

⇒ DB = 32