of 25 In the figure, PQ is parallel to RS. The length of PQ is 2 cm; the length of PR is 18 cm; the length...

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Question 23 of 25 In the figure, PQ is parallel to RS. The length of PQ is 2 cm; the length of PR is 18 cm; the length of QP is 27 cm. What is the length of SQ? A. 54 cm B. 3 cm C. 9 cm D. 63 cm

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Answer: C. 9 cmExplanation: Since PQ is parallel to RS, triangles PQR and SQR are similar by the Basic Proportionality Theorem (also known as Thales' theorem). Therefore, the sides are proportional:$ \frac{PQ}{RS} = \frac{PR}{SQ} $Substitute the known values:$ \frac{2}{RS} = \frac{18}{27} $Cross-multiply to solve for RS:$ 2 \times 27 = 18 \times RS $$ 54 = 18 \times RS $$ RS = \frac{54}{18} = 3 $Since RS is the entire length of SQ, the length of SQ is 9 cm.

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of 25 In the figure, PQ is parallel to RS. The length of PQ is 2 cm; the length of PR is 18 cm; the length...

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