I think you are missing something. We know that triangle ABC ~ ADE
So suppose the dilation factor of ADE/ABC is x, where x < 1
Then we know that AC = 15/x
and by the law of cosines,
(15/x)^2 = 16^2 + 20^2 - 2*16*20 cosB
Now, you can see that for any scale factor x<1, there is an angle B which will provide that DE can be 15 units long. All you need is cosB < 431/640
That is, any triangle ABC with B < 47.66° can provide a DE||AC with a length of 15.
In triangle ABC segment DE is parallel to side AC. What is the length of AD if AB=16cm and DE=15cm and AC=20cm
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