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 length of the pictures, we can divide the length by the width for each enlargement.
For the first enlargement: length = 16 cm, width = 24 cm, so the ratio is 16/24 = 0.67
For the second enlargement: length = 24 cm, width = 36 cm, so the ratio is 24/36 = 0.67
For the third enlargement: length = 32 cm, width = 48 cm, so the ratio is 32/48 = 0.67
For the fourth enlargement: length = 40 cm, width = 60 cm, so the ratio is 40/60 = 0.67
As we can see, the ratio is consistent at 0.67 for all enlargements.
Therefore, the constant of proportionality between the width and length of the pictures is A) 0.5.