1. **State the problem:** We have a triangle that is originally 4 inches tall and 3 inches wide. It is enlarged so that its height becomes 8 inches. We need to find the new width. 2. **Formula and rule:** When a shape is enlarged proportionally, all linear dimensions scale by the same factor. The scale factor is the ratio of the new height to the original height. 3. **Calculate the scale factor:** $$\text{scale factor} = \frac{\text{new height}}{\text{original height}} = \frac{8}{4} = 2$$ 4. **Apply the scale factor to the width:** $$\text{new width} = \text{original width} \times \text{scale factor} = 3 \times 2 = 6$$ 5. **Answer:** The new width of the triangle is 6 inches.