Question

Given: △PQR∼△JXY, QS and XZ are medians, PQ=9, XZ=4, QS=XJ.
Find: QS

Answer 1

Answer: 6 unit

Explanation:

Here, two triangle PQR and JXY are given,

In which QS and XZ are the medians of triangles PQR and JXY respectively,

Also,

`\triangle PQR \sim \triangle JXY`

Since, the corresponding sides and corresponding median of similar triangles are in same ratio,

`\implies (PQ)/(JX) = (QS)/(XZ)`

Here, PQ=9 unit , XZ=4 unit, QS=XJ unit,

`\implies (9)/(QS) = (QS)/(4)`

`\implies (QS)/(9) = (4)/(QS)`

`\implies QS* QS = 9* 4`

`\implies QS^2 = 36`

`\implies QS=6\text{ unit}`

Note : Since, it is the measurement of length, this is why we did not take √36 = - 6.