Dallas
Houston
San Antonio
3 in
3.75 in
4.125 in
Question content area bottom
Part 1
If the actual distance from San Antonio to Houston is approximately 188 miles, use the lengths of the line segments indicated in the figure along with similar triangles to approximate
a. the actual distance from Dallas to Houston.
b. the actual distance from Dallas to San Antonio.
To solve this problem, we can use the concept of similar triangles.
Given the lengths of the line segments in the figure:
- Distance from Dallas to Houston = 3.75 in
- Distance from San Antonio to Houston = 3 in
- Distance from San Antonio to Dallas = 4.125 in
We can set up a proportion to find the actual distances:
\( \frac{4.125}{3} = \frac{x}{3.75} \)
Solving for x, we get:
\( x = \frac{4.125}{3} \times 3.75 = 5.25 \)
Therefore, the actual distance from Dallas to Houston is approximately 5.25 miles.
To find the actual distance from Dallas to San Antonio, we can set up another proportion:
\( \frac{4.125}{3} = \frac{x}{5.25} \)
Solving for x, we get:
\( x = \frac{4.125}{3} \times 5.25 \approx 7 \)
Therefore, the actual distance from Dallas to San Antonio is approximately 7 miles.