Answer: AC= 10 cm and CE= 5 cm
Step-by-step explanation:
In the given picture, Δ ADE is a right triangle
∴ By Pythagoras theorem,
[tex]AD^2+DE^2=AE^2\\\Rightarrow\ (8+4)^2+9^2=AE^2\\\Rightarrow\ AE^2=12^2+9^2\\\Rightarrow\ AE^2=144+81=225\\\Rightarrow\ AE=15\ cm[/tex]
Since triangles ABC and ADE are similar and corresponding sides of similar triangles are proportional therefore,
[tex]\frac{AB}{AC}=\frac{AD}{AE}\\\Rightarrow\frac{8}{AC}=\frac{12}{15}\\\Rightarrow\ AC=\frac{8\times15}{12}\\\Rightarrow\ AC=10\ cm[/tex]
Now, AE=AC+CE
⇒CE=AE-AC
⇒CE=15-10=5 cm
