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?

Answer 1

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)) :}#

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.