Question

What value of x would make Bl parallel to RA?

Answer 1

Given:

Bl parallel to RA.

To find:

The value of x.

Solution:

In triangle ATR and ITB,

`\angle ATR\cong \angle ITB` [Common angles]

`\angle ART\cong \angle IBT` [Corresponding angle]

`\triangle ATR\sim \triangle ITB` [AA property of similarity]

We know that the corresponding sides of a similar triangle are proportional. So,

`(AT)/(IT)=(AR)/(IB)`

`(x)/(x+8)=(12)/(18)`

`(x)/(x+8)=(2)/(3)`

On cross multiplication, we get

`3(x)=2(x+8)`

`3x=2x+16`

`3x-2x=16`

`x=16`

Therefore, the correct option is C.