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A square with a perimeter of 137 units is the image of a square that was dilated by a scale factor of 4 . Find the perimeter of the preimage, the original square, before its dilation. Round your answer to the nearest tenth, if necessary. Answer: units

A square with a perimeter of 137137 units is the image of a square that was dilated by a scale factor of 44 . Find the perimeter of the preimage, the original square, before its dilation. Round your answer to the nearest tenth, if necessary.\newlineAnswer: units

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Q. A square with a perimeter of 137137 units is the image of a square that was dilated by a scale factor of 44 . Find the perimeter of the preimage, the original square, before its dilation. Round your answer to the nearest tenth, if necessary.\newlineAnswer: units
  1. Calculate Side Length: First, we need to understand that the perimeter of a square is four times the length of one side. Since the perimeter of the dilated square is 137137 units, we can find the length of one side of the dilated square by dividing the perimeter by 44.\newlineCalculation: Side length of dilated square = 137137 units // 44
  2. Find Original Side Length: Now, we divide 137137 by 44 to find the length of one side of the dilated square.\newlineCalculation: 137/4=34.25137 / 4 = 34.25 units
  3. Calculate Original Perimeter: Next, we use the scale factor to find the length of one side of the original square. The scale factor is given as 44, which means the side of the dilated square is 44 times longer than the side of the original square.\newlineCalculation: Side length of original square = Side length of dilated square / Scale factor = 34.2534.25 units / 44
  4. Final Answer: We calculate the side length of the original square.\newlineCalculation: 34.25/4=8.562534.25 / 4 = 8.5625 units
  5. Final Answer: We calculate the side length of the original square.\newlineCalculation: 34.25/4=8.562534.25 / 4 = 8.5625 unitsTo find the perimeter of the original square, we multiply the length of one side by 44.\newlineCalculation: Perimeter of original square = 4×4 \times Side length of original square = 4×8.56254 \times 8.5625 units
  6. Final Answer: We calculate the side length of the original square.\newlineCalculation: 34.25/4=8.562534.25 / 4 = 8.5625 unitsTo find the perimeter of the original square, we multiply the length of one side by 44.\newlineCalculation: Perimeter of original square = 4×4 \times Side length of original square = 4×8.56254 \times 8.5625 unitsWe perform the multiplication to find the perimeter of the original square.\newlineCalculation: 4×8.5625=34.254 \times 8.5625 = 34.25 units
  7. Final Answer: We calculate the side length of the original square.\newlineCalculation: 34.25/4=8.562534.25 / 4 = 8.5625 unitsTo find the perimeter of the original square, we multiply the length of one side by 44.\newlineCalculation: Perimeter of original square = 4×4 \times Side length of original square = 4×8.56254 \times 8.5625 unitsWe perform the multiplication to find the perimeter of the original square.\newlineCalculation: 4×8.5625=34.254 \times 8.5625 = 34.25 unitsSince the problem asks for the perimeter of the original square before dilation and rounding to the nearest tenth is not necessary because our answer is already in a tenth, we have our final answer.\newlineCalculation: The perimeter of the original square is 34.2534.25 units.

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