Answer: 6 unit
Step-by-step explanation:
Here, two triangle PQR and JXY are given,
In which QS and XZ are the medians of triangles PQR and JXY respectively,
Also,
[tex]\triangle PQR \sim \triangle JXY[/tex]
Since, the corresponding sides and corresponding median of similar triangles are in same ratio,
[tex]\implies \frac{PQ}{JX} = \frac{QS}{XZ}[/tex]
Here, PQ=9 unit , XZ=4 unit, QS=XJ unit,
[tex]\implies \frac{9}{QS} = \frac{QS}{4}[/tex]
[tex]\implies \frac{QS}{9} = \frac{4}{QS}[/tex]
[tex]\implies QS\times QS = 9\times 4[/tex]
[tex]\implies QS^2 = 36[/tex]
[tex]\implies QS=6\text{ unit}[/tex]
Note : Since, it is the measurement of length, this is why we did not take √36 = - 6.
