when enlargeing sn object, why does the area increase diffrently than the preminter?
When enlarging an object, the increase in area and perimeter typically occurs at different rates. This is because area is a function of the square of the dimensions, while perimeter is a function of the sum of the dimensions.
To understand why the area increases differently than the perimeter, consider the following example: Let's take a square with sides measuring 2 units. The area of the square is calculated by squaring the side length, so in this case, the area is 2 units multiplied by 2 units, which equals 4 square units. The perimeter is calculated by adding all the sides together, so in this case, the perimeter is 2 units + 2 units + 2 units + 2 units, which equals 8 units.
Now, let's enlarge the square by doubling its side length. The new square will have sides measuring 4 units. To calculate the area, we square the new side length, so the area is 4 units multiplied by 4 units, which equals 16 square units. As for the perimeter, we add all the sides together, so the perimeter is 4 units + 4 units + 4 units + 4 units, which equals 16 units.
Comparing the initial and enlarged squares, we see that the side length doubled and the perimeter doubled as well. However, the area quadrupled. This discrepancy occurs because when you increase the dimensions of an object, the impact on the area is squared, while the impact on the perimeter is linear.
In general, when enlarging an object, each dimension is multiplied by a constant factor. If the constant factor is denoted as "k," then the area will increase by a factor of k^2, while the perimeter will increase by a factor of k.
So, when enlarging an object, the area and perimeter increase differently because the area is a quadratic function of the dimensions, while the perimeter is a linear function of the dimensions.