Enlarge 6 in x 10 in picture to 3 feet x 4 feet.
What is the scale factor and how much of the space will be used?
6":3' = 6:36 = 1:6
10":4' = 10:48 = 5:24
so, use the smaller scale factor, and ((24/5)/6)^2 = 16/25 of the space will be used.
6 in expands to 36 in
that would be times 6
10 in expands to 48 in
that would be times 4.8
so the 10 inch dimension is limiting
and the scale ratio is 4.8
6*4.8 = 28.8 inches
so what is used is 28.8 in x 48 in
To find the scale factor, we need to compare the dimensions of the original picture (6 inches x 10 inches) to the dimensions of the enlarged picture (3 feet x 4 feet).
First, we need to convert the dimensions to the same unit of measurement. Since the original dimensions are in inches, let's convert the enlarged dimensions to inches as well. There are 12 inches in 1 foot, so 3 feet x 12 inches/foot = 36 inches and 4 feet x 12 inches/foot = 48 inches.
Now we can calculate the scale factor. The scale factor is the ratio of the corresponding dimensions in the original and enlarged pictures. In this case, the scale factor for the width is 36 inches (enlarged) / 6 inches (original) = 6, and the scale factor for the height is 48 inches (enlarged) / 10 inches (original) = 4.
Therefore, the scale factor is 6 for the width and 4 for the height.
To find how much of the space will be used by the enlarged picture, we need to calculate the area of both the original and enlarged pictures.
The original picture has an area of 6 inches (width) x 10 inches (height) = 60 square inches.
The enlarged picture has an area of 36 inches (width) x 48 inches (height) = 1728 square inches.
To find the percentage of space used, we can divide the area of the enlarged picture by the total area available and multiply by 100.
(1728 square inches / 60 square inches) x 100 = 2880%
Therefore, the enlarged picture will use 2880% of the space.
Please note that the results may need to be adjusted if you want to calculate the scale factor and amount of space used in a different manner, such as using the original or enlarged picture's perimeter or volume.