Answer:
Option D. AC= 10 cm and CE= 5 cm
Step-by-step explanation:
From the given figure two triangles ΔABC and ΔADE are similar and two lines BC║DE.
From these similar triangles we know
[tex]\frac{AB}{AD}=\frac{BC}{DE}=\frac{AC}{AE}[/tex]
[tex]\frac{8}{12}=\frac{BC}{9}=\frac{AC}{AE}[/tex]
Therefore [tex]\frac{AC}{AE}=\frac{8}{12}=\frac{2}{3}[/tex]
Or AC=[tex]\frac{2}{3}AE[/tex]
Now from pythagoras theorem
AE = √(AD²+ED²) = √(12²+9²) = √(144+81) =√225 = 15 cm
Since we know side AC = [tex]\frac{2}{3}AE[/tex]
= [tex]\frac{2}{3}\times 15[/tex]
= 10 cm
Therefore AC = 10 cm and AE = 15cm and CE = (15-10) = 5 cm
