Problem solving: Pythagoras' theorem: Annabel @ A wishes to visit friend Bertie @ B

Masaru

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Sep 6, 2013
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Annabel ant at A wishes to visit her friend Bertie beetle at B on the opposite corner of a block of cheese which is 30cm by 20cm by 20cm. What is the shortest distance Annabel must travel if she
a. Loves to eat cheese

b. Hates to eat cheese

(It is not necessary, but you can see the diagram at https://sites.google.com/site/bentl...-triangles/problem-solving-pythagoras-theorem)

I have no problem with a) above.
The answer is the square root of 20^2 + 20^2 + 30^2, which is about 41.2 cm.

However, the answer section of the textbook says that the answer for b) is 50 cm, which I do not understand.
How can the ant get to B by walking only 50 cm from A even though it is only the sum of the width and legth of the cheese?

My answer would be the square root of 20^2 + (30 +20)^2, which is about 53.9 cm because the ant hates eating cheese, which means that he can only walk on the surface of the cheese, so if you think of the cheese as a box and dismantle and flat it out, the distance from A to B would be the hypotenuse of the right angled triangle of the sides 20 cm and 50 cm, right?

I would much appreciate it if somone can help me understand why the answer is 50 cm, not 53.9 cm.

Thank you.

 
There is also the possibility of:

\(\displaystyle d=\sqrt{(20+20)^2+30^2}\text{ cm}=50\text{ cm}\)
 
Thank you.

There is also the possibility of:

\(\displaystyle d=\sqrt{(20+20)^2+30^2}\text{ cm}=50\text{ cm}\)

Oh, thank you very much.

I should have tried all possibilities - not only 1 or 2.
 
… the answer for b) is 50 cm, which I do not understand.
How can the ant get to B by walking only 50 cm from A even though it is only the sum of the width and legth of the cheese?
The ant is not restricted to walking along the edges; it can also cross any face diagonally.


… I should have tried all possibilities - not only 1 or 2.
Were you kinda guessing on each question? I'm curious whether you drew any diagram, at some point. :cool:
 
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