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
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.
To find the length of AD, we can use the concept of similar triangles.
In triangle ABC, segment DE is parallel to side AC. This indicates that triangle ADE is similar to triangle ABC. Therefore, the ratio of corresponding sides of these triangles will be equal.
We can set up a proportion using this information. Let's define x as the length of AD:
AD/AB = DE/AC
Substituting the given values:
x/16 = 15/20
Now, we can cross-multiply and solve for x:
20x = 16 * 15
20x = 240
x = 240/20
x = 12
Therefore, the length of AD is 12 cm.