A band poster that measures 90 cm by 40 cm is reduced by a scale factor of 1/6 so it can fit on a postcard.
a) What are the dimensions of the postcard image?
b) By what scale factor, to the nearest hundredth, was the area of the poster decreased in the reduction process?
a. Dimensions=90/8 by 40/8 = 11.25cm by 5cm.
b. A2/A1 = (11.25*5)/(90*40) = 64.
To find the dimensions of the postcard image, we need to apply the scale factor of 1/6 to the original dimensions of the band poster.
a) Dimension of the postcard image = (Scale Factor) x (Dimension of the poster)
Applying this formula:
Width of the postcard image = (1/6) x (90 cm) = 15 cm
Height of the postcard image = (1/6) x (40 cm) = 6.67 cm (rounded to nearest hundredth)
Therefore, the dimensions of the postcard image are approximately 15 cm by 6.67 cm.
b) To find the scale factor by which the area of the poster was decreased, we need to compare the original area with the new area.
Area of the original poster = (Length of the poster) x (Width of the poster)
Area of the original poster = 90 cm x 40 cm = 3600 cm^2
Area of the postcard image = (Length of the postcard image) x (Width of the postcard image)
Area of the postcard image = 15 cm x 6.67 cm = 100.05 cm^2 (rounded to nearest hundredth)
To find the scale factor, we can divide the new area by the original area:
Scale Factor = (Area of the postcard image) / (Area of the original poster)
Scale Factor = 100.05 cm^2 / 3600 cm^2 ≈ 0.0278 (rounded to nearest hundredth)
Therefore, the area of the poster was decreased by approximately 0.0278 or 2.78% in the reduction process.