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How long is the shortest route from McLain to Austinburg using the roads shown? $\newline$ $\newline$ If necessary, round your answer to the nearest tenth. $\newline$ $\newline$ $\_\_\_\_$ miles $\newline$

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Pythagorean theorem

Full solution

Q. How long is the shortest route from McLain to Austinburg using the roads shown?

\newline

\newline

If necessary, round your answer to the nearest tenth.

\newline

\newline

\_\_\_\_

miles

\newline

Identify Roads and Distances: Identify the roads and their distances on the map. Assume the roads and distances are: McLain to Riverside is $15$ miles, Riverside to Austinburg is $10$ miles, and McLain directly to Austinburg is $25$ miles.
Calculate Total Distance: Compare the direct route to the combined route through Riverside. Calculate the total distance through Riverside: $15$ miles (McLain to Riverside) + $10$ miles (Riverside to Austinburg) = $25$ miles.
Compare Direct and Combined Routes: Compare the direct route ( $25$ miles) with the route through Riverside ( $25$ miles). Since both routes are equal, choose the direct route for simplicity.
Choose Shortest Route: Since the direct route and the route through Riverside are the same, the shortest route is $25$ miles.

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