Final answer:
The scale factor for enlarging a 3 by 4 photo to a 15 by 20 size is 5. To calculate the scale factor, divide the dimensions of the enlarged size by those of the original size. With this scale factor, you can determine actual dimensions using a direct proportion, multiplying the scale dimension by the scale factor.
Step-by-step explanation:
To find the scale factor of an enlargement from a 3 by 4 photo to a 15 by 20 size, we can compare the lengths of corresponding sides. Since the scale factor should be consistent for both dimensions (length and width), let's choose one dimension to calculate the scale factor. For example, if we take the length (longer side) of both pictures, for the original photo it is 4, and for the enlarged photo, it is 20.
To find the scale factor, we divide the size of the enlarged photo by the size of the original photo:
Scale Factor = Enlarged size / Original size
Scale Factor = 20 / 4 = 5
Now that we know the scale factor is 5, this means that each dimension of the original photo is multiplied by 5 to achieve the new dimensions of the enlarged photo. An important thing to realize is that the scale dimensions and actual dimensions must be directly proportional.
Example:
If we have a scale dimension of 4 and a known scale factor of 5, we can find the actual dimension using a proportion:
Scale Factor:Actual Dimension = Scale Dimension:x
5:x = 4:x
To solve for x, we multiply both sides of the proportion by x and then divide by 5:
x = 4 times 5
x = 20
Therefore the actual dimension corresponding to the scale dimension of 4 (with a scale factor of 5) is 20.