Question

in the figure PQ is parallel to RS. the length of RP is 6 cm; the length of PT is 18 cm; the length of QT is 21 cm; what is the length of SQ?

Answer 1

Option A.
`SQ=7\ cm`

Explanation:

we know that

In the figure

The triangles PTQ and RTS are similar by AA Similarity Theorem

so

Remember that

If two figure are similar, then the ratio of its corresponding sides is equal

so

`(PT)/(RT)=(QT)/(ST)`

we have

`PT=18\ cm`

`RT=RP+PT=6+18=24\ cm`

`QT=21\ cm`

`SQ=ST-21\ cm` ------> equation A

substitute the values and solve for ST

`(18)/(24)=(21)/(ST)`

`ST=21*24/18`

`ST=28\ cm`

substitute the value of ST in the equation A to find the value of SQ

`SQ=28-21=7\ cm`