## A Crow Flies

A crow flies (always in straight line) from its nest $10$ miles north and $7$ miles east of the nest. At that point, it sees a scarecrow, and so it turns and flies to a point $4$ miles farther north and $5$ miles east. From there it flies directly back to the nest. To the nearest mile, what is the total distance the crow flies?
Source: NCTM Mathematics Teacher, October 2006

Solution

$AB^2=10^2+7^2=149$
$BC^2=4^2+5^2=41$
$AC^2=14^2+12^2=340$
$AB+BC+AC=\sqrt{149}+\sqrt{41}+\sqrt{340}=37.05$ miles
To the nearest mile, the crow flies a total distance of $37$ miles.

Answer: $37$ miles