To determine the length of the new road that will connect the service station to Cray, we first need to analyze the given information and possibly use some geometric methods depending on the figure. However, since the exact figure isn't provided here, I'll make an assumption based on standard scenarios involving points, distances, and roads forming a right triangle.
Let's consider a typical scenario where the given measurements could form a right triangle:
- One leg of the triangle represents the 5 miles distance from Cray to the highway.
- The other leg represents the 12 miles distance along the highway.
- The hypotenuse then will be the new road connecting Cray to the service station.
To find the length of the hypotenuse (the new road), we use the Pythagorean theorem:
\[ a^2 + b^2 = c^2 \]
where:
- \( a = 5 \) miles
- \( b = 12 \) miles
- \( c \) is the length of the new road
Let's plug in the values:
\[ 5^2 + 12^2 = c^2 \]
\[ 25 + 144 = c^2 \]
\[ 169 = c^2 \]
\[ c = \sqrt{169} \]
\[ c = 13 \] miles
Thus, the new road connecting the service station to Cray will be 13 miles long.
Given the available choices:
- 13 mi
- 5 mi
- 12 mi
- 40 mi
- 4.6 mi
- 31.2 mi
- 5.4 mi
The correct length of the new road is 13 mi.
However, among the provided options in your rephrased query (though 13 mi should have been an option considering the math), none seems to match this calculation. If you have a drawing that makes any measurements clearer or adjustments required within the problem context, please refer to that for a precise match.
Study the road plan shown in the figure. A service station will be built on the highway, and a road will connect it with Cray. How long will the new road be?
highway (13mi) 5mi 12mi
40 mi
4.6 mi
31.2 mi
5.4 mi
1 answer
2 answers