Recall that the ratio of the perimeters of the similar triangles is proportional to the scale factor.
≈633 miles
Practice makes perfect
Let's begin with recalling what we know about the perimeters of similar polygons.
If two polygons are similar, then their
perimeters are proportional to
the scale factor between them.
Since each distance on the map is proportional to the actual distance, the triangle formed by St.Louis, Springfield and Kansas City on the map is similar to the triangle formed by these cities in the real world.
Therefore, we can use the perimeter of the triangle on the map to find the perimeter of the actual triangle. Let's start with evaluating the perimeter of the triangle on the map.
15in.+10in.+13in.=38in.
Next we will use the fact that the scale of the map is 3in.= 50mi to create a proportion. Let P be the perimeter of the actual triangle.
3in./50mi=38in./P
Finally, we will solve the above proportion using cross multiplication.
