A photographer wants to print a photograph and two smaller copies on a rectangular sheet of paper. The larger photographer and the smaller photographs are in proportion. The larger photograph has a width of 4 inches and a length of 6 inches. Find the measurements of the small photographs for each diagram.
2 inches by 3 inches
4x6 = 8x12
Let's assume the width and length of the smaller photographs are represented by "w" and "l" respectively.
Since the larger photograph has a width of 4 inches and a length of 6 inches, we can set up the following proportion:
4/6 = w/l
To solve for "w" and "l", we need to find the ratio of the widths and lengths of the small photographs to the larger photograph.
Assuming the smaller photographs are printed as identical copies, the proportion can be simplified to:
2w/4 = l/6
Cross-multiplying, we get:
6(2w) = 4l
12w = 4l
Simplifying further, we can divide both sides by 4:
3w = l
Therefore, the width of the smaller photographs is represented by "w" and the length is represented by "3w".
To solve this problem, we need to determine the proportions between the larger photograph and the smaller ones, and then find the measurements of the small photographs.
Let's start by finding the proportional relationship between the larger photograph and the smaller ones. We know that the larger photograph has a width of 4 inches and a length of 6 inches. Let's assign variables to the width and length of the smaller photographs. We can use "w" for the width and "l" for the length.
Since the smaller photographs are in proportion with the larger photograph, we can set up the following ratio:
(width of smaller photograph) / (width of larger photograph) = (length of smaller photograph) / (length of larger photograph)
w / 4 = l / 6
Now, we can solve this equation for "w" and "l" by cross-multiplying:
6w = 4l
Divide both sides of the equation by 2 to simplify:
3w = 2l
Now, we have a ratio between the width and length of the small photographs.
To find the measurements of the small photographs, we need one more piece of information. Are the small photographs going to be printed next to each other horizontally or vertically?
Let's consider both scenarios:
1. If the small photographs are printed horizontally (side by side) on the rectangular sheet of paper:
Let's say each small photograph has a width of "x" inches. Since they are printed side by side, the total width will be 2x inches. According to the ratio we found above, the length of each small photograph will be (2/3)x inches.
So the measurements of each small photograph will be:
Width: x inches
Length: (2/3)x inches
2. If the small photographs are printed vertically (one on top of the other) on the rectangular sheet of paper:
Let's say each small photograph has a length of "y" inches. Since they are printed one on top of the other, the total length will be 2y inches. According to the ratio we found above, the width of each small photograph will be (3/2)y inches.
So the measurements of each small photograph will be:
Width: (3/2)y inches
Length: y inches
In summary, the measurements of the small photographs will depend on whether they are printed horizontally or vertically on the rectangular sheet of paper.
Horizontal printing:
Width of each small photograph: x inches
Length of each small photograph: (2/3)x inches
Vertical printing:
Width of each small photograph: (3/2)y inches
Length of each small photograph: y inches