In a triangle ABC segment DE parallel to side AC. (Endpoints like on AB and BC respectively.)

What is the length of AD if AB = 16 cm, AC = 20cm and DE = 15cm?

Question

In a triangle ABC segment DE parallel to side AC. (Endpoints like on AB and BC respectively.) 

What is the length of AD if AB = 16 cm, AC = 20cm and DE = 15cm?

directrix · Answer

Triangle BDE ~ Triangle BAC by the AA Postulate. 

Lengths of corresponding sides of similar triangle are in proportion.

BD/BA = DE/AC

BD/16 = 15/20

BD/16 = 3/4

Cross multiply and solve for BD.

Then, subtract BD from AB (16) to get the length of AD.
@victorlau123 

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