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,

$\dfrac{AT}{IT}=\dfrac{AR}{IB}$

$\dfrac{x}{x+8}=\dfrac{12}{18}$

$\dfrac{x}{x+8}=\dfrac{2}{3}$

On cross multiplication, we get

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

$3x=2x+16$

$3x-2x=16$

$x=16$

Therefore, the correct option is C.