Given Δ ABC ∼ Δ DEF.

Assertion (A): If area of Δ ABC = 64 cm², area of Δ DEF = 49 cm² and BC = 4 cm, then EF is 7 cm.

Reason (R): The ratio of area of two similar triangle is equal to the ratio of square of their corresponding sides.

1. Assertion (A) is true, but Reason (R) is false.

2. Assertion (A) is false, but Reason (R) is true.

3. Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

4. Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).

Given Δ ABC ∼ Δ DEF.

As we know that the ratio of area of two similar triangle is equal to the ratio of square of their corresponding sides.

So, reason (R) is true.

$\Rightarrow \dfrac{\text{area of ΔABC}}{\text{area of ΔDEF}} = \dfrac{BC^2}{EF^2} \\[1em] \Rightarrow \dfrac{64}{49} = \dfrac{4^2}{EF^2} \\[1em] \Rightarrow \dfrac{64}{49} = \dfrac{16}{EF^2} \\[1em] \Rightarrow EF^2 = \dfrac{49 \times 16}{64} \\[1em] \Rightarrow EF^2 = \dfrac{49}{4} \\[1em] \Rightarrow EF = \sqrt{\dfrac{49}{4}} \\[1em] \Rightarrow EF = \dfrac{\sqrt{49}}{\sqrt{4}} \\[1em] \Rightarrow EF = \dfrac{7}{2}.$

So, assertion (A) is false.

Thus, Assertion (A) is false, but Reason (R) is true.

Hence, option 2 is the correct option.