Question

A poster shop will enlarge a photograph into a poster. Given the size of the photograph and the length of the poster, what is the constant of proportionality? What is the width of the poster, x?

A. k = 4.5, 54 cm
B. k = 3.5, 42 cm
C. k = 6, 96 cm
D. k = 6, 72 cm

Answer 1

k = 72/16 = 4.5
12 x 4.5 = 54 cm

answer
A. k = 4.5, 54 cm

Answer 2

Option: A is the correct answer.

A. k = 4.5 , 54 cm

Explanation:

We know that the constant of proportionality is the fixed amount by which each of the dimensions of the figure are changed.

It is defined as ratio of the length of the side of the image to the corresponding side of the original image.

Here the original photograph has dimensions as:

12 cm and 16 cm

Now, the length of the enlarged poster is: 72 cm.

Hence,

`\text{Constant of proportionality}=(72)/(16)\\\\i.e.\\\\\text{Constant of proportionality}=4.5`

Now the width of the poster i.e. x= 4.5×12

i.e.

Width of poster= 54 cm.