Discussion

Explanation:

Given, ΔABC ~ ΔDEF

∴ The ratio of the areas of similar triangles is equal to ratio of the square of the their respective sides.

In the two similar triangles side BC in ∆ABC is corresponding to side EF in ∆DEF.

⇒ $\frac{Area\left(∆ABC\right)}{Area\left(∆DEF\right)}={\left(\frac{BC}{EF}\right)}^2$

⇒ $\frac{81}{144}={\left(\frac{BC}{9}\right)}^2$

⇒ $\frac{9}{12}=\frac{BC}{9}$

⇒ BC = 6.75

Hence, option (d).

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