Question

Help me plz find the value of x for which QR is parallel to RS

Answer 1

Given:

QR is parallel to RS.

To find:

The value of x.

Solution:

In the given figure, we have,

`PR=12`

`RT=2x-2`

`QS=21`

`ST=3x-1`

Using basic proportionality theorem (BPT), we get

`(PR)/(RT)=(QS)/(ST)`

`(12)/(2x-2)=(21)/(3x-1)`

On cross multiplication, we get

`12(3x-1)=21(2x-2)`

`36x-12=42x-42`

`36x-42x=12-42`

`-6x=-30`

Divide both sides by -6.

`x=(-30)/(-6)`

`x=5`

Therefore, the value of x is 5.