Gretchen is using an overhead projector to enlarge a drawing so she can make a poster. The original drawing measures 60 mm wide by 80 mm high. She moves the projector so that the width of the projected image is 300 mm. If the original drawing and the projected image are similar figures, what will be the height of the projected image?
440 mm
400 mm
225 mm
180 mm
The width of the original drawing is 60 mm and the width of the projected image is 300 mm. Since the original drawing and the projected image are similar figures, the ratio of corresponding sides will be the same.
Let x be the height of the projected image. Since the ratio of width to height for the original drawing is 60:80 = 3:4, the ratio of width to height for the projected image will also be 3:4.
Thus, 300:x = 3:4
Cross multiplying, we get:
4 * 300 = 3 * x
1200 = 3x
x = 400 mm
Therefore, the height of the projected image will be 400 mm.
Answer: 400 mm