Joe has a picture that measures 8 centimeters by 12 centimeters. He creates four enlargements of the picture. The table below shows the width and the length of each enlargement.
What is the constant of proportionality between the width and the length of the pictures?
Responses
A 0.50.5
B 1.21.2
C 1.51.5
D 2.5
To find the constant of proportionality between the width and the length of the pictures, we first need to consider what it means. The constant of proportionality between two quantities is a value that describes how much one quantity changes in relation to another. For lengths and widths that are proportional, this constant is the ratio of the length to the width (or vice versa). In this case, we can look at the original picture's dimensions to determine that constant.
Given:
Original width = 8 cm
Original length = 12 cm
To find the constant of proportionality (k), we divide the length by the width:
k = Length / Width = 12 cm / 8 cm = 1.5
So the constant of proportionality between the width and the length of the pictures is 1.5. This applies to all the enlargements as well, provided that they are indeed proportional to the original picture. The correct answer is:
C 1.5