Question

Given the following segment lengths, find the length of segment AB.

AC=22mm
EC=44mm
ED=11mm
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Answer 1

5.5

Explanation:

Since BD is parallel to AE

=> AB/AC = ED/EC

AB/22 = 11/44

AB = 1/4(22)

AB = 5.5

Answer 2

The length of segment AB is 5.5 mm.

Explanation:

As segment BD is parallel to segment AE (as indicated by the arrows on the line segments), use the the Side Splitter Theorem for similar triangles to determine the length of segment AB.

Similar Triangles - Side Splitter Theorem

If a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.

Therefore, according to the Side Splitter Theorem:

`\implies \sf AB : AC = ED : EC`

`\implies \sf AB : 22 = 11 : 44`

`\implies \sf (AB)/(22) = (11)/(44)`

`\implies \sf (AB)/(22) \cdot 22= (11)/(44) \cdot 22`

`\implies \sf AB= (242)/(44)`

`\implies \sf AB= 5.5`

Therefore, the length of segment AB is 5.5 mm.