Question
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REASONING Triangles and are similar. Which statement is correct? Select all that apply.
(A)
(B)
©
(D)
7. USING STRUCTURE Rectangle is similar to rectangle . Rectangle has side lengths of 6 anc 12. Rectangle has a side length of 18 . What are the possible values for the length of the other side rectangle B? Select all that apply.
(A) 6
(B) 9
© 24
(D) 36

Ask by Frazier Ford. in the United States
Jan 29,2025

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Tutor-Verified Answer

Answer

For similar triangles, the correct statements are (A) and (B). For similar rectangles, the possible lengths for the other side are (B) 9 and (D) 36.

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Bonus Knowledge

If triangles and are similar, then all corresponding sides are in proportion. This means that:
  • Statement (A) is correct because follows the similarity ratio.
  • Statement (B) is incorrect as it mixes the sides without maintaining the correct proportional ratios.
  • Statement © is incorrect because it reverses the order of sides.
  • Statement (D) is incorrect due to incorrect side pairings.
For the rectangles, since rectangle has side lengths 6 and 12, we find the ratio of similarity to rectangle whose one side is given as 18. The ratio is . Therefore, the other side of rectangle must maintain this ratio relative to 6.
Possible calculations lead us to:
  • If the shorter side of rectangle matches with 6 (so: ), it is valid.
  • The side length that can give the ratio is therefore it’s correct.
  • The options 24 and 36 do not maintain the ratio of the rectangles, making them incorrect.
Thus, the correct values for the other side of rectangle B are:
(A) 6 and (B) 9.

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