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?
please and thank you
90/6 x 40/6 = 15 x 6.3
1/6^2 = 1/36 = 0.03
To find the dimensions of the postcard image and the scale factor by which the area of the poster was decreased, we can follow these steps:
Step 1: Find the dimensions of the postcard image:
The poster's dimensions are given as 90 cm by 40 cm. To reduce it by a scale factor of 1/6, we need to multiply each dimension by the scale factor.
Length of the postcard image = 90 cm * (1/6) = 15 cm
Width of the postcard image = 40 cm * (1/6) = 6.67 cm (rounded to two decimal places)
Therefore, the dimensions of the postcard image are approximately 15 cm by 6.67 cm.
Step 2: Calculate the scale factor for the area reduction:
The scale factor for area reduction can be found by comparing the areas of the poster and the postcard image.
Area of the original poster = length * width = 90 cm * 40 cm = 3600 cm²
Area of the postcard image = length * width = 15 cm * 6.67 cm = 100.05 cm² (rounded to two decimal places)
To find the scale factor, divide the area of the poster by the area of the postcard image:
Scale factor = Area of the poster / Area of the postcard image
= 3600 cm² / 100.05 cm²
≈ 35.99 (rounded to two decimal places)
Therefore, the scale factor, to the nearest hundredth, by which the area of the poster was decreased is approximately 35.99.