Answer:
The sides of △DEF are DE = 1.5cm, DF = 3cm, and EF= 2.25 cm.
Step-by-step explanation:
We know that
[tex]\triangle ABC \sim \triangle DE\ F[/tex]
[tex]AB=2cm\\BC=3cm\\CA=4cm\\DE=1.5cm[/tex]
Remember that a similarity between two triangles represent a proportional relation between corresponding side. In this case, such proportions are
[tex]\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}[/tex]
So, we have to find sides DF and EF. Using given values, we have
[tex]\frac{AB}{DE}=\frac{BC}{EF}\\ \frac{2}{1.5}=\frac{3}{EF}\\ EF=\frac{3(1.5)}{2}=2.25[/tex]
Then,
[tex]\frac{AB}{DE}=\frac{AC}{DF}\\\frac{2}{1.5}=\frac{4}{DF}\\ \\DF=\frac{4(1.5)}{2}=3[/tex]
Therefore, the sides of △DEF are DE = 1.5cm, DF = 3cm, and EF= 2.25 cm.
