Question

A river flows between two houses A and B, the houses standing some distances away from the banks. Where should a bridge be built on the river so that a person going from A to B, using the bridge to cross the river may do so by the shortest path? Assume that the banks of the river are straight and parallel, and the bridge must be perpendicular to the banks.

Answer 1

@Kitt020912 @nathan917

Answer 2

@Mertsj

Answer 3

If you draw an imaginary line connecting the two houses, the bridge should start where the line touches the bank for the first time.

Answer 4

ok

Answer 5

Or.


Solution: Let coincide the river banks. means let width of river is zero
the river will be appear as a straight line.
Join A to B by straight line this line will intersect river line at P, so this will be required length,
Now when u separated the river banks point P will be aparted by points p' and p'' . so these points are place where we need to make bridge.
In other words we need points on bridge which makes equal angles to A and other side B .... there shud be two similar tingles.

Answer 6

you can think of this problem as follows:

the bridge has to be crossed, so we cannot change that distance.
therefore, just shrink the width of the river to zero and proceed as shown by @nathan917 to the solution.

Answer 7

ok

Answer 8

@nathan917
Something like this? o.O