Short cut

Imagine that you are going to the friend. That path has a length 120 meters. Then turn doprava and go another 630 meters and you are at a friend's.

The question is how much the journey will be shorter if you go direct across the field?

Correct result:

x =  108.7 m

Solution:

a=120 m b=630 m  c0=a+b=120+630=750 m  c12=a2+b2  c1=a2+b2=1202+630230 457 m641.3267 m  x=c0c1=750641.3267=108.7 ma=120 \ \text{m} \ \\ b=630 \ \text{m} \ \\ \ \\ c_{0}=a+b=120+630=750 \ \text{m} \ \\ \ \\ c_{1}^2=a^2 + b^2 \ \\ \ \\ c_{1}=\sqrt{ a^2 + b^2 }=\sqrt{ 120^2 + 630^2 } \doteq 30 \ \sqrt{ 457 } \ \text{m} \doteq 641.3267 \ \text{m} \ \\ \ \\ x=c_{0}-c_{1}=750-641.3267=108.7 \ \text{m}

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