landscaping company is hired to construct a triangular jarden in a park. In order to plan the dimensions of the jarden, the company created a scale model of the three sides of the scale model are 9 inches, 2 inches, and 18 inches. If the largest side length of the jarden will be 24 feet, what will be the perimeter, in feet, f the completed garden?

To solve the problem, we need to determine the perimeter of the completed garden based on the dimensions of the scale model. ### Step 1: Identify the scale of the model The sides of the scale model are given as 9 inches, 2 inches, and 18 inches. The largest side of the model is 18 inches. The largest side of the completed garden is 24 feet. We need to convert this to inches for consistency: \[ 24 \text{ feet} = 24 \times 12 \text{ inches} = 288 \text{ inches} \] ### Step 2: Calculate the scale factor Now, we can find the scale factor by comparing the largest side of the model to the largest side of the garden: \[ \text{Scale factor} = \frac{\text{Largest side of the garden}}{\text{Largest side of the model}} = \frac{288 \text{ inches}}{18 \text{ inches}} = 16 \] ### Step 3: Scale the other sides Next, we will scale the other sides of the model using the scale factor of 16: - For the side measuring 9 inches: \[ 9 \text{ inches} \times 16 = 144 \text{ inches} \] - For the side measuring 2 inches: \[ 2 \text{ inches} \times 16 = 32 \text{ inches} \] - For the side measuring 18 inches (already calculated): \[ 18 \text{ inches} \times 16 = 288 \text{ inches} \] ### Step 4: Calculate the perimeter of the garden Now, we can find the perimeter of the completed garden by adding the scaled sides: \[ \text{Perimeter} = 144 \text{ inches} + 32 \text{ inches} + 288 \text{ inches} = 464 \text{ inches} \] ### Step 5: Convert the perimeter to feet Finally, we convert the perimeter from inches to feet: \[ \text{Perimeter in feet} = \frac{464 \text{ inches}}{12} \approx 38.67 \text{ feet} \] Thus, the perimeter of the completed garden is approximately \(38.67\) feet.