Distance$/$Similarity Measures $(10$ points$)$

Given the four boxes shown in the following figure, answer the following questions. In the

diagram, numbers indicate the lengths and widths and you can consider each box to be a vector

of two real numbers, length and width. For example, the top left box would be $(2,1),$ while the

bottom right box would be $(3,3).$ Restrict your choices of similarity$/$distance measure to

Euclidean distance and correlation. Please explain your choice.

Which proximity measure would you use to group the boxes based on their shapes $($length$-$width

ratio$)?$

Which proximity measure would you use to group the boxes based on their size?