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

Answer: C. 3cm

Explanation:

Answer 2

Step 1

Find the value of TS

we know that

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

so

`(TR)/(TP) =(TS)/(QT)`

solve for TS

`TS =(TR*QT)/(TP)`

we have

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

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

substitute

`TS =(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`