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

Answer:

Option A. k = 4.5, 54 cm

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and this ratio is called the scale factor

In this problem the constant of proportionality is equal to the scale factor

step 1

Find the scale factor

Let

k -----> the constant of proportionality

$k=\frac{72}{16}=4.5$ -----> ratio of the corresponding sides

step 2

Find the value of x

$\frac{72}{16}=\frac{x}{12}\\\\x=4.5(12)\\\\x=54\ cm$

therefore

k = 4.5, 54 cm