VMO 2018 Problem 3

An investor has two rectangular pieces of land of size $120\times 100$ . a. On the first land, she want to build a house with a rectangular base of size $25\times 35$ and nines circular flower pots with diameter $5$ outside the house. Prove that even the flower pots positions are chosen arbitrary on the land, the remaining land is still sufficient to build the desired house. b. On the second land, she want to construct a polygonal fish pond such that the distance from an arbitrary point on the land, outside the pond, to the nearest pond edge is not over $5$ . Prove that the perimeter of the pond is not smaller than $440-20\sqrt{2}$ .