Help with distance question points A and B

Question

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Ok. I had no idea how to do the question but I tried fiddling with the triangles to see if I can get any value but only managed to get $MN$. I read the solution to this question, and it said that I should make $M$ coincide with $N$ so that we get $AMB$ as a straight line. I understood that, but then it said that $AMB$ is the hypotenuse of a right angled triangle with sides length of 5 and 12. How is one of the sides 5? shouldn't it be 3 as in the photo?

Let the opposite banks of the river approach each other until they coincide. The $5$ is $3+2$. — André Nicolas, Mar 27 '14 at 20:43

score 1 · Accepted Answer · answered Mar 27 '14 at 20:48

The basic idea is to eliminate the river from the picture. Euclid's axiom tells you that the shortest distance between any two points (here, $A,B$) lies along the straight line through them. Here, the line segment $AB$ would be the hypotenuse of the right-angled triangle with sides $12$ and $2+3=5$.

Help with distance question points A and B

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