Final answer:
To find the longer side of the actual room, establish the scale factor using the model's measurements and the actual perimeter, convert units for consistency, and calculate the length and width. Afterward, identify which is greater and convert that number back to feet to find the longer side.
Step-by-step explanation:
You've asked about finding the length of the longer side of an actual room, given that the room has a perimeter of 340 feet, and the measured sides of a scaled-down model are 5.8 cm and 2.7 cm. To solve this, we need to determine the scale of the model and then use this scale to find the actual dimensions of the room.
First, let's find the scale factor by using the perimeter. Since the actual room's perimeter is 340 feet, and we want to find the scale in reference to the model's sides, we need to find two numbers that, when doubled and added (since there are two lengths and two widths in a rectangle), will equal 340 feet. These will be the actual room's length and width in feet.
However, since there's an inconsistency in measuring units (the model's dimensions are in cm while the actual room's dimensions are in feet), we'll need to convert one of them for a proper comparison. Let's assume the model uses the same scale for length and width and convert the feet to centimeters to maintain consistency with the model's measurements (1 foot = 30.48 cm). Multiplying 340 feet by 30.48 gives us the perimeter in centimeters.
Next, since we have a rectangle, we know the formula to find the perimeter is Perimeter = 2 * (length + width). We will set the sum of twice the model's length and twice the model's width equal to the scaled-up perimeter in centimeters and solve for the actual length and width.
Once we have the actual lengths in centimeters, we can convert them back into feet to find the length of the longer side. We'll take the larger of the two numbers after converting them to feet, which would then give us the longer side of the actual room.