A college professor was using a projector to give his lectures. A slide whose dimensions are 11 inches wide and seven inches high was projected into an image that was 53 and half inches wide. Find the height of the projected image.
Let’s begin by sketching the slide whose dimensions are 11 inches wide and seven inches high. We are told that this was projected into an image that was 53 and half inches wide. We have been asked to calculate the heights of the projected image in inches. We will call this ℎ. The slide and the image are similar rectangles. This means that the image is an enlargement or dilation of the slide. We need to multiply the dimensions of the slide by a scale factor to give us the dimensions of the image.
Another way of thinking about this is that the ratio of the corresponding sides must be equal. The ratio of the heights ℎ over seven must be equal to the ratio of the widths 53 and half over 11. The mixed number 53 and half is equal to 107 over two. Dividing this by 11 gives us 107 over 22. ℎ over seven is equal to 107 over 22.
We can then multiply both sides of our equation by seven such that ℎ is equal to 107 over 22 multiplied by seven. This is equal to 749 over 22. Dividing 749 by 22 gives us 34 remainder one. This means that the height of the projected image is 34 and one over 22 inches.