Playground volleyball area

In Kocourkov, they decided to build a children's playground and volleyball courts. The volleyball court will have dimensions of 18 m x 19 m. The playground will have a square shape. The area of both fields will be the same. What will be the dimensions of the playground?

Final Answer:

x =  18.4932 m

Step-by-step explanation:

$$\begin{gathered} a=18\text{m} \\ b=19\text{m} \\ {S}_1=a\cdot b=18\cdot 19=342{\text{m}}^2 \\ {S}_2=S_1=342{\text{m}}^2 \\ {S}_2=x\cdot x=x^2 \\ x=\sqrt{S_2}=\sqrt{342}=3\sqrt{38}=18.4932\text{m} \end{gathered}$$

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