Loading…
Example 8.79 from Elementary Algebra, 8.7 Solve Proportion and Similar Figure Applications
Solve Proportion and Similar Figure Applications: example 8.79
On a map, San Francisco, Las Vegas, and Los Angeles form a triangle whose sides are shown in the figure below. If the actual distance from Los Angeles to Las Vegas is 270 miles find the distance from Los Angeles to San Francisco.
Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.
Solution
Read the problem. Draw the figures and label with the given information. The figures are shown above. Identify what we are looking for. The actual distance from Los Angeles to San Francisco. Name the variables. Let distance from Los Angeles to San Francisco. Translate into an equation. Since the triangles
are similar, the corresponding sides are
proportional. We'll make the numerators
"miles" and the denominators "inches."Solve the equation. Check. On the map, the distance from Los Angeles to
San Francisco is more than the distance from
Los Angeles to Las Vegas. Since 351 is more
than 270 the answer makes sense.Answer the question. The distance from Los Angeles to San Francisco is 351 miles.
Your turn
The book's Try It right after this example: same idea, new numbers. Only the answer is given.
On the map, Seattle, Portland, and Boise form a triangle whose sides are shown in the figure below. If the actual distance from Seattle to Boise is 400 miles, find the distance from Seattle to Portland.
How did it go?