1. **State the problem:** We have triangle DEF formed by connecting the midpoints of the sides of triangle ABC. We know the side lengths of triangle DEF are 2, 3, and 4. We need to find the perimeter of triangle ABC. 2. **Recall the midpoint theorem:** The triangle formed by joining the midpoints of the sides of a triangle is similar to the original triangle and each side of the smaller triangle is half the length of the corresponding side of the original triangle. 3. **Apply the theorem:** Since D, E, and F are midpoints, each side of triangle DEF is half the length of the corresponding side of triangle ABC. 4. **Calculate the sides of triangle ABC:** If the sides of DEF are 2, 3, and 4, then the sides of ABC are: $$ \text{Side of ABC} = 2 \times \text{Side of DEF} $$ So, $$ \text{Sides of ABC} = 2 \times 2 = 4, \quad 2 \times 3 = 6, \quad 2 \times 4 = 8 $$ 5. **Find the perimeter of triangle ABC:** The perimeter is the sum of all sides: $$ P_{ABC} = 4 + 6 + 8 = 18 $$ **Final answer:** The perimeter of triangle ABC is 18.