Question$\triangle A B C$ and $\triangle D E F$ are similar. The length of the smallest side of $\triangle A B C$ is 2 units and the length of the smallest side of $\triangle D E F$ is 5 units. The area of $\triangle A B C$ is 4 units squared. What is the area, in units squared, of $\triangle D E F$ ? F. 8 G. 10 H. 15 J. 18 K. 25

Studdy Solution
Use the scale factor to find the area of $\triangle DEF$:
The area of similar triangles is proportional to the square of the scale factor:
$$\text{Area of } \triangle DEF = \text{Area of } \triangle ABC \times k^2$$ $$= 4 \times \left(\frac{5}{2}\right)^2$$ $$= 4 \times \frac{25}{4}$$ $$= 25$$
The area of $\triangle DEF$ is:
$$\boxed{25}$$