Answer:
x = 3, y = 6
Step-by-step explanation:
In the figure attached,
If ΔADE and ΔABC are similar triangles, their corresponding sides will be in the same ratio.
By this property,
[tex]\frac{AB}{AD}=\frac{AC}{AE}=\frac{BC}{DE}[/tex]
[tex]\frac{AB}{AD}=\frac{AC}{AE}[/tex]
[tex]\frac{AD+BD}{AD}=\frac{AE+EC}{AE}[/tex]
[tex]\frac{3}{2}=\frac{x+1.5}{x}[/tex]
3x = 2x + 3
3x - 2x = 3
x = 3
Similarly, [tex]\frac{AB}{AD}=\frac{BC}{DE}[/tex]
[tex]\frac{3}{2}=\frac{y}{4}[/tex]
y = [tex]\frac{3\times 4}{2}[/tex]
y = 6
