Answer:
The side of square A'B'C'D' is 16 inches
Explanation:
Given
Length of Square ABCD = 4 inches
Dilated with a scale factor of 4
Required
Length of square A'B'C'D'
To dilate something means to enlarge or reduce the size of that thing, depending on the scale factor.
Consider the following conditions
- When the scale factor is greater than 1, then the size of new shape will be bigger than the dilated shape
- When the scale factor is equal to 1, the new shape will maintain the same size as the dilated shape
- When the scale factor is less than 1 but greater than 0, the size of new shape will be smaller than that of the dilated shape.
Having mentioned the conditions of dilation, Here, the "thing being dilated" is a square (ABCD) on a scale factor of 4.
The scale factor is greater than 1; so, the new shape (A'B'C'D) will be bigger than the previous shape (ABCD)
Now, how is the new size calculated?
The new size is calculated by multiplying the length of the previous shape by its scale factor;
In other words,
New Length = Old Length * Scale Factor
Where
Old Length = Length of ABCD = 4 inches
Scale Factor = 4
By Substitution,
New Length = 4 inches * 4
New Length = 16 inches
Hence, the side of square A'B'C'D' is 16 inches