Original scale: 1 inch = 8 feet. A parallelogram with a side length of 24 feet. A larger parallelogram with a side length of 72 feet. Noah planned a parallelogram-shaped sidewalk to lead from the street to the front door of his house. He realized the walkway was too short and he needs to change the length to 72 feet. He wrote a ratio to find the change in the scale factor. 24 ft 72 ft = The change in the scale factor is . The change of scale means that 1 inch represented feet, but now 1 inch represents feet.
Question
Original scale: 1 inch = 8 feet. A parallelogram with a side length of 24 feet. A larger parallelogram with a side length of 72 feet. Noah planned a parallelogram-shaped sidewalk to lead from the street to the front door of his house. He realized the walkway was too short and he needs to change the length to 72 feet. He wrote a ratio to find the change in the scale factor.
24 ft 72 ft
The change in the scale factor is . The change of scale means that 1 inch represented feet, but now 1 inch represents feet.
Solution
The original scale is 1 inch = 8 feet. This means that on the original plan, 1 inch represented 8 feet of the actual sidewalk.
The length of the sidewalk on the original plan was 24 feet. This means that on the original plan, the sidewalk was 24/8 = 3 inches long.
Noah wants to change the length of the sidewalk to 72 feet. To find out how long this would be on the plan, we can set up a ratio:
24 feet : 3 inches = 72 feet : x inches
Cross-multiplying gives us 24x = 216, so x = 9 inches.
This means that on the new plan, the sidewalk will be 9 inches long.
The change in the scale factor is then 9 inches / 72 feet = 1 inch / 8 feet.
So the scale has not changed: 1 inch still represents 8 feet.
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