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Triangle A has sides of lengths #75 #, #45 #, and #54 #. Triangle B is similar to triangle A and has a side of length #7 #. What are the possible lengths of the other two sides of triangle B?

Answer 1

Aurora Ayala

Possible lengths of other two sides of triangle B are
#8(2/5)=8.4# & #11(2/3)=11.667#

Triangles A & B are similar. #:.7/45=b/54=c/75# #b=(7*54)/45=42/5=8(2/5)=8.4# #c=(7*75)/45=35/3=11(2/3)=11.667#

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Answer 2

Autumn Armstrong

Since triangles (A) and (B) are similar, their corresponding sides are in proportion. Let (x) be the length of one side of triangle (B), which corresponds to the side of length (75) in triangle (A).

Using the ratio of corresponding sides of similar triangles:

[ \frac{75}{7} = \frac{45}{y} = \frac{54}{z} ]

Solving for (y) and (z) gives:

[ y = \frac{45 \times 7}{75} = \frac{21}{5} \times 7 = 21 ]

[ z = \frac{54 \times 7}{75} = \frac{18}{5} \times 7 = 12.6 ]

Therefore, the possible lengths of the other two sides of triangle (B) are (21) and (12.6).

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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.