Triangle A has sides of lengths #12 #, #16 #, and #8 #. Triangle B is similar to triangle A and has a side with a length of #16 #. What are the possible lengths of the other two sides of triangle B?
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The other two sides of #b# could be
#color(black)({21 1/3, 10 2/3}) or color(black)({12,8}) or color(black)({24,32})#
#{:
("sides of "A,,"|",color(blue)(12),"|",color(green)(16),"|",color(cyan)(8)),
(,"option",,,,,,),
("possible sides of "B,[1],"|",color(magenta)(16),"|",color(magenta)(16)/color(blue)(12) * color(green)(16) = 21 1/3,"|", color(magenta)(16)/color(blue)(12) * color(cyan)(8) = 10 2/3),
(,[2],"|",color(red)(16)/color(green)(16) * color(blue)(12) = 12,"|",color(red)(16),"|",color(red)(16)/color(green)(16) * color(cyan)(8) = 8),
(,[3],"|",color(orange)(16)/color(cyan)(8) * color(blue)(12) = 24,"|",color(orange)(16)/color(cyan)(8) * color(green)(16) = 32,"|",color(orange)(16))
:}#
