To find the height of the original triangle when it has been reduced by a scale factor of 0.4, we can set up the relationship between the dimensions of the original triangle and the reduced triangle.
Let \( h \) be the height of the original triangle. When the triangle is reduced by a scale factor of 0.4, the height of the reduced triangle becomes:
\[ \text{Height of reduced triangle} = h \times 0.4 \]
We need to compare the reduced triangle to the given rectangle, which has a height of 2 inches. To find the height of the original triangle, we will consider the height of the reduced triangle (which must be equal to the height of the rectangle).
Thus, we have:
\[ h \times 0.4 = 2 \]
Now, we can solve for \( h \):
\[ h = \frac{2}{0.4} \]
Calculating the right side gives:
\[ h = \frac{2}{0.4} = \frac{20}{4} = 5 \]
Thus, the height of the original triangle is \( \boxed{5} \) inches.
1 answer