To find the width of the larger rectangle that maintains the same aspect ratio as the smaller rectangle, we can set up a proportion based on the ratios of the dimensions.
The aspect ratio of the smaller rectangle is given by its length and width: \[ \text{Aspect Ratio} = \frac{\text{Length}}{\text{Width}} = \frac{3.4}{5.7} \]
For the larger rectangle, we know the length is 17. Let the width of the larger rectangle be \( W \). We can set up the following equation using the aspect ratio: \[ \frac{3.4}{5.7} = \frac{17}{W} \]
Now, we can cross-multiply to solve for \( W \): \[ 3.4 \cdot W = 5.7 \cdot 17 \] Calculating \( 5.7 \cdot 17 \): \[ 5.7 \cdot 17 = 96.9 \]
Now substituting back: \[ 3.4W = 96.9 \]
Next, we divide both sides by 3.4 to find \( W \): \[ W = \frac{96.9}{3.4} \approx 28.5 \]
Thus, the width of the larger rectangle is approximately \( 28.5 \).