Answer:
[tex]x=2\ cm[/tex]
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
[tex]\frac{BA}{CA}=\frac{AE}{AD}[/tex]
we have
[tex]BA=10\ cm\\CA=(x+10)\ cm\\AE=15\ cm\\AD=15+3=18\ cm[/tex]
substitute the values
[tex]\frac{10}{x+10}=\frac{15}{18}[/tex]
solve for x
[tex]10(18)=15(x+10)\\180=15x+150\\15x=180-150\\15x=30\\x=2\ cm[/tex]
therefore
There is only one value of x that makes BAE and CAD triangles similar
