Question

In the figure, PQ is parallel to RS. The length of RP is 2 cm; the length of PT is 18 cm; the length of QT is 27 cm. What is the length of SQ?

Answer 1

Step 1    

Find the value of TS

we know that

if PQ is parallel to RS. then triangles TRS and TPQ are similar

so

$\frac{TR}{TP} =\frac{TS}{QT}$

solve for TS

$TS =\frac{TR*QT}{TP}$

we have

$RP=2\ cm\\TP=18\ cm\\QT=27\ cm$

$TR=TP+RP\\TR=18+2=20\ cm$

substitute

$TS =\frac{20*27}{18}$  

$TS =30\ cm$

Step 2

Find the value of SQ

we know that

$SQ=TS-QT$

we have

$TS =30\ cm$

$QT=27\ cm$

substitute

$SQ=30\ cm-27\ cm=3\ cm$

therefore

the answer is

the value of SQ is $3\ cm$

Answer 2

Answer: C. 3cm

Step-by-step explanation: