The Garcia family is going to remodel their basement. The basement floor has an area of 470 square feet On the blueprint, the basament has an area of 75.2 square inches. The perimeter of the basement on the blueprint is 348 inches. What is the perimeter of the real basement? for full credit, you must: - Show all your work. - Round your answer to the nearest tenth of a foot.

To find the perimeter of the real basement, we will first determine the scale factor between the real basement and the blueprint. Let's start with converting the areas from square feet to square inches. 1. **Convert the area of the real basement:** - \( 1 \text{ square foot} = 144 \text{ square inches} \) - \( 470 \text{ sq ft} = 470 \times 144 = 67,680 \text{ sq inches} \) 2. **Calculate the scale factor:** - The scale factor for the area is given by the ratio of the area on the blueprint to the real area. - Scale factor = \( \sqrt{\frac{\text{Area of real basement}}{\text{Area of blueprint}}} = \sqrt{\frac{67,680}{75.2}} \) Now let's calculate that. \[ \sqrt{\frac{67,680}{75.2}} = \sqrt{898.416} \approx 29.983 \] So the scale factor is approximately 29.983:1. 3. **Find the perimeter of the real basement:** - The perimeter of the blueprint is 348 inches. To get the real perimeter, multiply it by the scale factor. - Real perimeter = \( 348 \text{ inches} \times 29.983 \approx 10,428.834 \text{ inches} \) 4. **Convert the real perimeter to feet:** - Since \( 1 \text{ foot} = 12 \text{ inches} \): - Real perimeter in feet = \( \frac{10,428.834}{12} \approx 869.0695 \text{ feet} \) 5. **Round to the nearest tenth of a foot:** - Rounding \( 869.0695 \text{ feet} \) gives us \( 869.1 \text{ feet} \) **Final Answer: The perimeter of the real basement is approximately 869.1 feet.**