Short cut

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

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

Final Answer:

x =  108.7 m

Step-by-step explanation:

$$\begin{gathered} a=120\text{m} \\ b=630\text{m} \\ {c}_0=a+b=120+630=750\text{m} \\ {c}_1^2=a^2+b^2 \\ {c}_1=\sqrt{a^2+b^2}=\sqrt{120^2+630^2}=30\sqrt{457}\text{m}\doteq 641.3267\text{m} \\ x=c_0-c_1=750-641.3267=108.7\text{m} \end{gathered}$$

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