In the figure, `PS=3`, `SQ=6`, `QR=5`, `PT=x` and `TR=y`. Give any two pairs of values of `x` and `y` such that line `ST||` side `QR`.

Explanation

In `DeltaPQR`,
line `ST||` side `QR` ………..(Given)
`:.` by basic proportionally theorem,
`(PS)/(SQ)=(PT)/(TR)`
`:.(3)/(6)=(x)/(y)`
`:.(1)/(2)=(x)/(y)`
`:.y=2x`
Consider `x=2`, then `y=2xx2=4`
`:.` When `x=2` , then `y=4` is one possibility
Consider `x=2.5`, then `y=2xx2.5=5`
`:.` When `x=2.5`, then `y=5` is the other possibility
Note : while selecting the values of `x` and `y` the student needs to be careful as the sum of the lengths of two sides of a triangle is greater than lengths of the third side.
`:.x=` and `y=2` cannot be possible though it satisfies the equation `y=2x`.