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The figure below represents four linked routes as $ A $ and $ B $ cities. Review a picture and indicate a correct alternative: enter image description here

a) The path is shorter II

b) Path II is less than III

c) Path III is shorter than IV

d) Path II is shorter than IV

e) Paths I, II, III and IV are of equal length.

Solution: enter image description here

All paths have lengths equal to the sum $ (a + b)$ of the following rectangle triangle collars: This solution does not make much sense to me. He has not proved anything!

Lambert macuse
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  • Are the lines painted on a grid? – Bman72 Nov 12 '19 at 20:18
  • @Bman72 I dont know! The '' solution '' is just this – Lambert macuse Nov 12 '19 at 20:19
  • Because if they were on a grid you could say that to go from A to B, you'd have to go $n$ times left and $m$ times right. Doesn't matter which way you choose. But the picture is kind of misleading in my opinion – Bman72 Nov 12 '19 at 20:26
  • If you look at the cross in the Swiss flag (or the Red Cross flag, doesn't matter which), do you know why its circumference is the same as that of a square with the same width and height? If you look at that until it clicks, this problem will follow shortly thereafter. – Arthur Nov 12 '19 at 20:26
  • @Arthur Please explain to me what you just said? I don't understand how I can relate this to the problem ... – Lambert macuse Nov 12 '19 at 20:30

2 Answers2

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Hint: consider path I; at the second corner, imagine to draw a rectangle with the sides next to the second corner. What can you see?

egreg
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Here is why first route equals to $(a+b)$, and similar for the rest: enter image description here

Ethan
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  • Can you explain your drawing a little? – Lambert macuse Nov 12 '19 at 20:49
  • @JeffersonNascimento try to move each length on the blue route to the line segment $a$, also move each length on the orange route to the line segement $b$, you will find they have the same length – Ethan Nov 12 '19 at 20:51