A man wishes to reach the island in the middle of an ornamental lake without getting wet. The island is 20 feet from each edge of the pond (see diagram) and he has two planks each 19 feet long. How does he get across?

civonamzuk
May 26, 2015

#2**+15 **

From any vertex, he puts each end of one plank slightly less than about √[361/2] ft from this vertex so that both ends are supported on dry land.

Then he carries the other plank to the middle of this one and lays it down so that it connects with the corresponding vertex of the island......at the middle of this first plank, he is √[361 /4] ft from the beginning vertex......and the distance from this vertex this point to the island is slightly more than [20√2 - √[361/4] ft = 18.784 ft.......so it can be easily be spanned by the other 19 foot plank......!!! {i.e, he stays dry.....}

Here's a pic of the situation starting from the lower left vertex..... AB is the first plank, CE is the distance from the middle of this plank to the island vertex.....

CPhill
May 27, 2015

#2**+15 **

Best Answer

From any vertex, he puts each end of one plank slightly less than about √[361/2] ft from this vertex so that both ends are supported on dry land.

Then he carries the other plank to the middle of this one and lays it down so that it connects with the corresponding vertex of the island......at the middle of this first plank, he is √[361 /4] ft from the beginning vertex......and the distance from this vertex this point to the island is slightly more than [20√2 - √[361/4] ft = 18.784 ft.......so it can be easily be spanned by the other 19 foot plank......!!! {i.e, he stays dry.....}

Here's a pic of the situation starting from the lower left vertex..... AB is the first plank, CE is the distance from the middle of this plank to the island vertex.....

CPhill
May 27, 2015

#4**0 **

Point D [located at (0,0)] is the bottom left corner (vertex) of the lake..... point "E" [located at 20, 20] is the lower left vertex of the island.....between D and E is the water......and AB is the plank laid across the water anchored at both ends on dry land.....

The second plank - 19 ft long - spans CE = the distance [ about 18.78 ft ] from the middle of the first plank to the lower left vertex of the island

CPhill
May 27, 2015

#7**0 **

Your pic... It is a dark red car!! Maybe those glasses of yours are a tad too dark! :/

Are you trying to confuse the h**l out of me? It is working !! :))

Melody
May 27, 2015