Lake or pond

The landlord has a square lake. Trees grow around this lake. The lake wants to enlarge the pond twice and does not want to cut down or flood any tree.

How will he do that?

Result

x =  0

Solution:

S1=a2 S2=πr2  2⋅ S1=S2 2⋅ a2=πr2  r=a⋅ 2/π  h2=2⋅ h1 x=0S_{1}=a^2 \ \\ S_{2}=\pi r^2 \ \\ \ \\ 2 \cdot \ S_{1}=S_{2} \ \\ 2 \cdot \ a^2=\pi r^2 \ \\ \ \\ r=a \cdot \ \sqrt{ 2/\pi } \ \\ \ \\ h_{2}=2 \cdot \ h_{1} \ \\ x=0

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