To find the width of the larger similar rectangle, we can use the concept of similar figures, which states that the ratios of corresponding lengths of similar figures are equal.
First, let's calculate the ratio of the lengths of the two rectangles:
\[ \text{Ratio} = \frac{\text{Length of larger rectangle}}{\text{Length of smaller rectangle}} = \frac{17 , \text{ft}}{3.4 , \text{ft}} \]
Calculating the ratio:
\[ \frac{17}{3.4} = 5 \]
This means the larger rectangle is 5 times the size of the smaller rectangle.
Now, we can find the width of the larger rectangle by multiplying the width of the smaller rectangle by the same ratio:
\[ \text{Width of larger rectangle} = \text{Width of smaller rectangle} \times \text{Ratio} \]
Given that the width of the smaller rectangle is 5.7 ft:
\[ \text{Width of larger rectangle} = 5.7 , \text{ft} \times 5 \]
Calculating this gives:
\[ 5.7 \times 5 = 28.5 , \text{ft} \]
Therefore, the width of the larger rectangle is 28.5 ft.