Question 167
An investor has two rectangular lands, each of size $120 \times 100$.
a. On the first land, she wants to build a house with a rectangular base of size $25 \times 35$ and nine circular flower pots with diameter $5$ outside the house. Prove that for all positions of the flower pots, the remaining land is still sufficient to build the desired house.
b. On the second land, she wants 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 $440 - 20\sqrt{2}$.
a. On the first land, she wants to build a house with a rectangular base of size $25 \times 35$ and nine circular flower pots with diameter $5$ outside the house. Prove that for all positions of the flower pots, the remaining land is still sufficient to build the desired house.
b. On the second land, she wants 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 $440 - 20\sqrt{2}$.