Triangle A has sides of lengths #12 ,24 #, and #16 #. Triangle B is similar to triangle A and has a side of length #8 #. What are the possible lengths of the other two sides of triangle B?

Answer 1

Three possibilities are there. Three sides are either (A) #8, 16# and #10 2/3# or (B) #4, 8# and #5 1/3# or (C) #6, 12# and #8#.

The sides of triangle A are #12, 24# and #16# and triangle B is similar to triangle A with a side of length #8#. Let other two sides be #x# and #y#. Now, we have three possibilities. Either

#12/8=24/x=16/y# then we have #x=16# and #y=16xx8/12=32/3=10 2/3# i.e. three sides are #8, 16# and #10 2/3#

or #12/x=24/8=16/y# then we have #x=4# and #y=16xx8/24=16/3=5 1/3# i.e. three sides are #4, 8# and #5 1/3#

or #12/x=24/y=16/8# then we have #x=6# and #y=12# i.e. three sides are #6, 12# and #8#

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Answer 2

Caroline Aucoin

The possible lengths of the other two sides of Triangle B are 16 and 32.

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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.