A square has side length of 4.3 in . If the area is multiplied by 4
, what happens to the perimeter?

Question

A square has side length of 4.3 in . If the area is multiplied by 4 , what happens to the perimeter?

UpStudy AI · Accepted Answer

To determine what happens to the perimeter when the area of a square is multiplied by 4, we need to understand the relationship between the area and the perimeter of a square.

Given:
- Side length of the square = 4.3 inches

The area of a square is given by the formula:
$$ \text{Area} = \text{side length}^2 $$

The perimeter of a square is given by the formula:
$$ \text{Perimeter} = 4 \times \text{side length} $$

When the area is multiplied by 4, the new area is:
$$ \text{New Area} = 4 \times \text{Original Area} $$

Since the area is multiplied by 4, the side length of the square will also be multiplied by 2 (because the area is the square of the side length). Therefore, the new side length will be:
$$ \text{New Side Length} = 2 \times \text{Original Side Length} $$

Now, we can calculate the new perimeter using the new side length:
$$ \text{New Perimeter} = 4 \times \text{New Side Length} $$

Let's calculate the new perimeter.
Calculate the value by following steps:
- step0: Calculate:
  $$4\times 4.3$$
- step1: Multiply the numbers:
  $$17.2$$
The new side length is 8.6 inches.

Now, let's calculate the new perimeter:
$$ \text{New Perimeter} = 4 \times 8.6 $$

$$ \text{New Perimeter} = 34.4 \text{ inches} $$

Therefore, when the area of a square is multiplied by 4, the perimeter is also multiplied by 4.
When the area of a square is multiplied by 4, the perimeter is also multiplied by 4.

A square has side length of 4.3 in . If the area is multiplied by 4
, what happens to the perimeter?

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