# 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?

Result

x =  108.7 m

#### Solution:

$a=120 \ \text{m} \ \\ b=630 \ \text{m} \ \\ \ \\ c_{0}=a+b=120+630=750 \ \text{m} \ \\ \ \\ c_{1}^2=a^2 + b^2 \ \\ \ \\ c_{1}=\sqrt{ a^2 + b^2 }=\sqrt{ 120^2 + 630^2 } \doteq 30 \ \sqrt{ 457 } \ \text{m} \doteq 641.3267 \ \text{m} \ \\ \ \\ x=c_{0}-c_{1}=750-641.3267 \doteq 108.6733 \doteq 108.7 \ \text{m}$

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