Question 159
A farmer has 2 rectangle lands of size $120 \text{ m} \times 100 \text{ m}$.
a. On the first land, there are 9 circle gardens of diameter $5 \text{ m}$. Prove that regardless of the positions of the gardens, he can always build a rectangle garden of size $25 \text{ m} \times 35 \text{ m}$.
b. On the second land, he builds a convex polygon lake such that the shortest distance from any point on the boundary of the land to the lake is at most $5$ m. Prove that the perimeter of the lake is at least $440 - 20\sqrt{2}$ m.
a. On the first land, there are 9 circle gardens of diameter $5 \text{ m}$. Prove that regardless of the positions of the gardens, he can always build a rectangle garden of size $25 \text{ m} \times 35 \text{ m}$.
b. On the second land, he builds a convex polygon lake such that the shortest distance from any point on the boundary of the land to the lake is at most $5$ m. Prove that the perimeter of the lake is at least $440 - 20\sqrt{2}$ m.