Negative and postcard

The image on the negative has dimensions of 36x24 mm and is enlarged to a postcard format of 13.5x9 cm. In what proportion have the lengths increased? In what proportion has the image content increased?

Correct answer:

k =  15:4
q =  225:16

Step-by-step explanation:

$$\begin{gathered} x_1=36\text{ mm } \\ {x}_2=13.5\text{ cm}\to \text{ mm}=13.5\cdot 10\text{ mm}=135\text{ mm } \\ {y}_1=24\text{ mm } \\ {y}_2=9\text{ cm}\to \text{ mm}=9\cdot 10\text{ mm}=90\text{ mm } \\ k=x_2\mathrm{/}{x}_1=135\mathrm{/}36={\displaystyle \frac{15}{4}}=3\frac{3}{4}=3.75=15:4 \\ \text{ Verifying Solution: } \\ {k}_1=y_2\mathrm{/}{y}_1=90\mathrm{/}24={\displaystyle \frac{15}{4}}=3\frac{3}{4}=3.75 \end{gathered}$$

$q=k\cdot k=3.75\cdot 3.75={\displaystyle \frac{225}{16}}=14\frac{1}{16}=14.0625=225:16$

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