Question

What is AE? Enter your answer in the box.

Answer 1

Answer:

$AE=20\ units$

Step-by-step explanation:

we know that

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

In this problem

Triangles AEB and DEC are similar by AA Similarity Theorem

so

$\frac{AB}{DC}=\frac{AE}{DE}$

substitute the given values and solve for x

$\frac{10}{4}=\frac{2x+10}{x+3}$

Multiply in cross

$10x+30=8x+40\\10x-8x=40-30\\2x=10\\x=5$

Find the length side AE

$AE=2x+10$

substitute the value of x

$AE=2(5)+10=20\ units$