Answer:

"As AB = 3 cm and BC = 4 cm, AC = AB + BC = 3 + 4 = 7 cm.

Since ABC ∼ DEF, we can write the proportion:

AC/DE = AB/EF

7/4.5 = 3/EF

Cross multiplying and solving for EF, we get:

EF = (3 * 4.5) / 7 = 6.5 cm

So, the measure of EF is 6.5 cm, which is option (D).

The measure of side EF is 6 cm.

Given:

triangle ABC is similar to triangle DEF

AB = 3 cm

BC = 4 cm

DE = 4.5 cm

To Find:

we need to find the measure of the side EF

Solution:

we know that when two triangles are similar, the ratio of their corresponding sides is equal

as ABC ∼ DEF

⇒ AB/DE = BC/EF = CA/FD

substituting the values into the equation, we get-

3/4.5 = 4/EF

30/45 = 4/EF

EF = 4 × 45/30

EF = 4 × 3/2

EF = 2 × 3

EF = 6

Thus, the measure of side EF is 6 cm.

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