Triangle A has sides of lengths #24 #, #16 #, and #20 #. 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

#96/5 \ & \ 64/5\ \ or \ \ 24 \ \ & \ \ 20 \ \ \ or \ \ \ 32/3 \ \ & \ \ 40/3#

Let #x# & #y# be two other sides of triangle B similar to triangle A with sides #24, 16, 20#.

The ratio of corresponding sides of two similar triangles is same.

Third side #16# of triangle B may be corresponding to any of three sides of triangle A in any possible order or sequence hence we have following #3# cases

Case-1:

#\frac{x}{24}=\frac{y}{16}=\frac{16}{20}#

#x=96/5, y=64/5#

Case-2:

#\frac{x}{24}=\frac{y}{20}=\frac{16}{16}#

#x=24, y=20#

Case-3:

#\frac{x}{16}=\frac{y}{20}=\frac{16}{24}#

#x=32/3, y=40/3#

hence, other two possible sides of triangle B are

#96/5 \ & \ 64/5\ \ or \ \ 24 \ \ & \ \ 20 \ \ \ or \ \ \ 32/3 \ \ & \ \ 40/3#

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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.