Final answer:
The reduced photograph that is 2 inches wide will be 2.8 inches long, maintaining the original aspect ratio of 5:7.
Step-by-step explanation:
The question is asking about the proportions of a photograph that is being reduced in size. Since the original photo is 5 inches wide and 7 inches long and needs to be reduced to 2 inches wide, we need to calculate the new length while maintaining the aspect ratio of the photograph. The aspect ratio is the ratio of the width to the length, which for the original photo is 5:7.
To find the reduced length, we can set up a proportion:
Let x represent the unknown new length of the reduced photo.
The proportion is 5/7 = 2/x as the ratio of width to length must remain constant.
Solving for x, we multiply both sides by x and get 5x = 2 × 7.
Now, dividing both sides by 5 to solve for x, we find x = (2 × 7)/5.
Calculating this gives us x = 2.8, so the reduced photo is 2.8 inches long.
Hence, the reduced photo is 2 inches wide by 2.8 inches long.