Question

Triangles △ABC and △DEF are similar. Find the lengths of the sides of △DEF, if AB=2 cm, BC=3 cm, CA=4 cm, DE=1.5 cm.

Answer 1

Answer:

DF=3.0cm, EF=3cm

Step-by-step explanation:

Given: ΔABC is similar to ΔDEF,

Therefore: $\frac{AB}{DE} =\frac{AC}{DF}$

            ⇒$\frac{2}{1.5}= \frac{4}{DF}$

            ⇒ DF=3.0cm

Now, by the similarity of triangles, we have Ef=3cm.

Answer 2

Answer:

The sides of △DEF are DE = 1.5cm, DF = 3cm, and EF= 2.25 cm.

Step-by-step explanation:

We know that

$\triangle ABC \sim \triangle DE\ F$

$AB=2cm\\BC=3cm\\CA=4cm\\DE=1.5cm$

Remember that a similarity between two triangles represent a proportional relation between corresponding side. In this case, such proportions are

$\frac{AB}{DE}=\frac{BC}{EF}=\frac{AC}{DF}$

So, we have to find sides DF and EF. Using given values, we have

$\frac{AB}{DE}=\frac{BC}{EF}\\ \frac{2}{1.5}=\frac{3}{EF}\\ EF=\frac{3(1.5)}{2}=2.25$

Then,

$\frac{AB}{DE}=\frac{AC}{DF}\\\frac{2}{1.5}=\frac{4}{DF}\\ \\DF=\frac{4(1.5)}{2}=3$

Therefore, the sides of △DEF are DE = 1.5cm, DF = 3cm, and EF= 2.25 cm.