24)If ∆ABC is similar to ∆DEF such that BC = 3 cm, EF = 4 cm and area of ∆ABC = 54 cm². Find the area of ∆DEF.

24)If ∆ABC is similar to ∆DEF such that BC = 3 cm, EF = 4 cm and area of ∆ABC = 54 cm². Find the area of ∆DEF.

Answer: Since the ratio of area of two similar triangles is equal to the ratio of the squares of any two corresponding sides, we have

\(\frac{\text{Area}(\triangle ABC)}{\text{Area}(\triangle DEF)} = \frac{BC^2}{EF^2}\)

\(\frac{54}{\text{Area}(\triangle DEF)} = \frac{3^2}{4^2} = \frac{9}{16}\)

\(\text{Area}(\triangle DEF) = \frac{16 \times 54}{9} = 16 \times 6 = 96 \text{ cm}^2\)