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

$\dfrac{PR}{RT}=\dfrac{QS}{ST}$

$\dfrac{12}{2x-2}=\dfrac{21}{3x-1}$

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.

$x=\dfrac{-30}{-6}$

$x=5$

Therefore, the value of x is 5.