Question

Help me understand this question

Answer 1

Answer:

$x=2\ cm$

see the explanation

Step-by-step explanation:

we know that

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

In this problem

Triangle BAE and CAD are similar -----> given problem

so

using proportionality

$\frac{BA}{CA}=\frac{AE}{AD}$

we have

$BA=10\ cm\\CA=(x+10)\ cm\\AE=15\ cm\\AD=15+3=18\ cm$

substitute the values

$\frac{10}{x+10}=\frac{15}{18}$

solve for x

$10(18)=15(x+10)\\180=15x+150\\15x=180-150\\15x=30\\x=2\ cm$

therefore

There is only one value of x that makes BAE and CAD triangles similar