Asked by bob
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
Answers
Answered by
oobleck
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.
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.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.