Answer :
To solve the problem using a proportion, follow these steps:
1. Understand the scale: According to the given scale, 3 centimeters on the map represent 11 kilometers in reality.
2. Set up a proportion: We need to find the actual length of the trail given that it measures 9.7 centimeters on the map. So, we set up the proportion like this:
[tex]\[
\frac{3 \text{ cm}}{11 \text{ km}} = \frac{9.7 \text{ cm}}{x \text{ km}}
\][/tex]
Where [tex]\( x \)[/tex] is the actual length of the trail in kilometers.
3. Solve the proportion: Cross-multiply to find [tex]\( x \)[/tex]:
[tex]\[
3 \times x = 11 \times 9.7
\][/tex]
[tex]\[
3x = 106.7
\][/tex]
4. Divide to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{106.7}{3}
\][/tex]
[tex]\[
x \approx 35.5667
\][/tex]
The actual length of the trail is approximately 35.6 kilometers.
So, the correct choice is 35.6 km.
1. Understand the scale: According to the given scale, 3 centimeters on the map represent 11 kilometers in reality.
2. Set up a proportion: We need to find the actual length of the trail given that it measures 9.7 centimeters on the map. So, we set up the proportion like this:
[tex]\[
\frac{3 \text{ cm}}{11 \text{ km}} = \frac{9.7 \text{ cm}}{x \text{ km}}
\][/tex]
Where [tex]\( x \)[/tex] is the actual length of the trail in kilometers.
3. Solve the proportion: Cross-multiply to find [tex]\( x \)[/tex]:
[tex]\[
3 \times x = 11 \times 9.7
\][/tex]
[tex]\[
3x = 106.7
\][/tex]
4. Divide to solve for [tex]\( x \)[/tex]:
[tex]\[
x = \frac{106.7}{3}
\][/tex]
[tex]\[
x \approx 35.5667
\][/tex]
The actual length of the trail is approximately 35.6 kilometers.
So, the correct choice is 35.6 km.
