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A square has side length of 7.3 in. If the area is multiplied by
, what happens to the perimeter?
The perimeter is tripled.
The perimeter is multiplied by 9.
The perimeter is multiplied by .
The perimeter is multiplied by .

Ask by Wood O'Quinn. in the United States
Mar 18,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The perimeter is multiplied by .

Solution

  1. Let the side length of the square be inches. The area is and the perimeter is .
  2. The problem states that the area is multiplied by . Therefore, the new area is:
  3. If the new side length is , then:
    Taking the square root of both sides gives:
  4. The new perimeter is :
  5. Comparing the new perimeter to the original perimeter , we have:
  6. Thus, the perimeter is multiplied by .

Answered by UpStudy AI and reviewed by a Professional Tutor

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Beyond the Answer

When you multiply the area of a square by , you are essentially reducing the area. The area of the square is given by side length squared, so in this case, it’s which equals about 53.29 in². Reducing the area by gives an area of approximately 5.91 in². To find the new side length, you take the square root of the new area, leading to a reduced side length of around 2.43 in.
Now, the perimeter is calculated as four times the side length. So originally, the perimeter was in. Now, with the side length reduced to 2.43 in, the new perimeter is in, which means the perimeter is multiplied by . So, the correct answer is that the perimeter is multiplied by !

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