1. **Problem Statement:** We are given a rectangular garden with length 150 m and breadth 100 m. There is a 3 m wide walking path around the inside of the garden. 2. **Step 1: Understand the problem and draw a proportional diagram.** - The garden is a rectangle 150 m by 100 m. - The walking path is inside the garden, 3 m wide all around. - So, the inner rectangle (garden minus walking) has length $150 - 2 \times 3 = 144$ m and breadth $100 - 2 \times 3 = 94$ m. 3. **Step 2: Calculate the area of the walking path.** - Area of the whole garden: $$150 \times 100 = 15000 \text{ m}^2$$ - Area of the inner rectangle (without walking): $$144 \times 94 = 13536 \text{ m}^2$$ - Area of walking path = Area of garden - Area of inner rectangle $$15000 - 13536 = 1464 \text{ m}^2$$ 4. **Step 3: Calculate the perimeter of the garden and find the side of the square house.** - Perimeter of rectangular garden: $$2(150 + 100) = 2 \times 250 = 500 \text{ m}$$ - The square house has the same perimeter, so side length of square house: $$\text{side} = \frac{500}{4} = 125 \text{ m}$$ 5. **Step 4: Calculate the area of the square house floor.** - Area = side$^2$ = $$125^2 = 15625 \text{ m}^2$$ 6. **Step 5: Calculate the number of tiles needed to cover the floor.** - Each tile covers 25 m$^2$. - Number of tiles = $$\frac{15625}{25} = 625$$ tiles. **Final answers:** - Area of walking path = 1464 m$^2$ - Number of tiles needed = 625