Area of triangle ADE = 9 cm² and area of trapezium DBCE = 16 cm².

Statement (1) : $\dfrac{\text{DE}}{\text{BC}} = \dfrac{3}{4}$.

Statement (2) : $\dfrac{\text{ΔADE}}{\text{ΔABC}} = \dfrac{9}{25} \Rightarrow \dfrac{\text{DE}}{\text{BC}} = \dfrac{3}{5}$.

1. Both the statement are true.

2. Both the statement are false.

3. Statement 1 is true, and statement 2 is false.

4. Statement 1 is false, and statement 2 is true.

Given,

Area of triangle ADE = 9 cm² and area of trapezium DBCE = 16 cm².

In Δ ABC and Δ ADE,

⇒ ∠BAC = ∠DAE (Common angle)

⇒ ∠ABC = ∠ADE (Corresponding angles are equal)

⇒ ∠ACB = ∠AED (Corresponding angles are equal)

∴ Δ ABC ∼ Δ ADE (By A.A.A. postulate)

From figure,

⇒ Area of triangle ABC = Area of triangle ADE + Area of trapezium DBCE = 9 + 16 = 25 cm²

We know that,

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides.

$\therefore \dfrac{\text{Area of Δ ADE}}{\text{Area of Δ ABC}} = \dfrac{DE^2}{BC^2}\\[1em] \Rightarrow\dfrac{9}{25} = \dfrac{DE^2}{BC^2}\\[1em] \Rightarrow \dfrac{DE}{BC} = \sqrt{\dfrac{9}{25}} = \dfrac{3}{5}$

So, statement 1 is false but statement 2 is true.

Hence, option 4 is the correct option.