Pokemon to the rescue

Geometry Level 5

Ash and his Pokémon are on a recon mission to save a city. They start off at point A A which is the origin. The city is at the point B = ( 18 , 0 ) . B=(18, 0). They want to get there as fast as possible but there are dark forests (shaped in quadrilaterals) in the way. The corners of Forest 1 are ( 1 , 1 ) , ( 1 , 1 ) , ( 9 , 1 ) (1, 1), (1, -1), (9, -1) and ( 9 , 1 ) . (9, 1). Those of Forest 2 are ( 11 , 1 ) , ( 11 , 1 ) , ( 17 , 1 ) (11, 1), (11, -1), (17, -1) and ( 17 , 1 ) . (17, 1). Between these forests, there is a safehouse, namely point C = ( 10 , 0 ) . C=(10,0).

Now, since the dark forests are ruled by unknown monsters, the Pokémon crew want to keep 1 units distance away from them. With these conditions, how much distance do they have to cover if they have to get to point B B and back with the shortest amount of travel but also have to stay at the safehouse on the way there and back? Round your answer to the nearest integer.


The answer is 49.

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2 solutions

Sai Swetha Kv
Apr 29, 2014

All straight line distances for the way up = 1 + 8 + 1 + 1 + 6 + 1 1+8+1+1+6+1 . All sectors of radius 1 = π 2 \frac { \pi }{ 2 } ... there are 4 sectors that equals 2 π 2\pi Thus, complete distance the way forward = 18 + 2 π 18+2\pi

On the way back the same..

Complete distance traveled = 2 ( 18 + 2 π ) = 2 ( 18 + 2 ( 3.14 ) ) = 48.6 49 2(18+2 \pi )= 2(18+2(3.14))= 48.6 \cong 49 That's the answer!

It took a while for someone to actually answer the question. Great solution, but try to use latex. People can read it better.

Sharky Kesa - 7 years, 1 month ago

could u explain y ur taking sectors into consideration when u hav already calculated that its 18

light antony - 7 years, 1 month ago

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because when you're maintaining a constant distance from the corner of the jungle you move in an arc centered at the corner of the jungle! And i's 18 + 2 π 18+2\pi .. I just learnt latex sorry!

Sai Swetha KV - 7 years, 1 month ago
Ahmad Saad
Nov 27, 2015

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