To find the base length of the drawing, we need to maintain the same proportions between the original flag and the scale drawing.
The original dimensions of the flag are:
- Base length = 21 inches
- Height = 49 inches
Dillon's scale drawing has a height of 14 inches. We can find the scale factor by comparing the height of the drawing to the height of the original flag:
\[ \text{Scale factor} = \frac{\text{Height of drawing}}{\text{Height of original}} = \frac{14 \text{ inches}}{49 \text{ inches}} = \frac{14}{49} = \frac{2}{7} \]
Since the scale factor is \(\frac{2}{7}\), we can find the base length of the drawing by applying the same scale factor to the original base length:
\[ \text{Base length of drawing} = \text{Base length of original} \times \text{Scale factor} = 21 \text{ inches} \times \frac{2}{7} \]
Calculating this:
\[ \text{Base length of drawing} = 21 \text{ inches} \times \frac{2}{7} = \frac{21 \times 2}{7} = \frac{42}{7} = 6 \text{ inches} \]
Thus, the base length of Dillon's drawing is 6 inches.