Photo paper format

The digital photo has dimensions of 640 × 480 pixels. Which of the classic photo paper formats is "most similar": 9 x 6 cm, 10 x 7 cm, 13 x 9 cm, 15 x 10 cm, 18 x 13 cm, or 30 x 20 cm?

Final Answer:

x = 18:13

Step-by-step explanation:

$$\begin{gathered} r=640:480\doteq 1.3333=4:3 \\ {r}_1=9:6=1.5=3:2 \\ {r}_2=10:7\doteq 1.4286=10:7 \\ {r}_3=13:9\doteq 1.4444=13:9 \\ {r}_4=15:10=1.5=3:2 \\ {r}_5=18:13\doteq 1.3846=18:13 \\ {r}_6=30:20=1.5=3:2 \\ {\Delta }_1=|r-r_1|=|1.3333-1.5|=\frac{1}{6}\doteq 0.1667 \\ {\Delta }_2=|r-r_2|=|1.3333-1.4286|=\frac{2}{21}\doteq 0.0952 \\ {\Delta }_3=|r-r_3|=|1.3333-1.4444|=\frac{1}{9}\doteq 0.1111 \\ {\Delta }_4=|r-r_4|=|1.3333-1.5|=\frac{1}{6}\doteq 0.1667 \\ {\Delta }_5=|r-r_5|=|1.3333-1.3846|=\frac{2}{39}\doteq 0.0513 \\ {\Delta }_6=|r-r_6|=|1.3333-1.5|=\frac{1}{6}\doteq 0.1667 \\ min{\Delta }_5 \\ x=18:13 \end{gathered}$$

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