Question

What is DE?
Enter your answer as a decimal in the box
12.6
units

Answer 1

`DE=6.3\ units`

Explanation:

see the attached figure to better understand the problem

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

Triangles ABC and DBE are similar by AA Similarity Theorem

so

`(AC)/(DE)=(AB)/(DB)=(BC)/(BE)`

we have

`AC=12.6\ units`

`AB=2DB`

substitute

`(12.6)/(DE)=(2DB)/(DB)/tex]</p><p>Simplify</p><p>[tex](12.6)/(DE)=2`

`DE=12.6/2\\DE=6.3\ units`