Question

What is the value of x, given that Line of PQ║line BC?
A. 26
B. 15
C. 13
D. 11

Answer 1

Line of PQ║line BC

6/12 = x/26

1/2 = x/26

x = 26 / 2

x = 13

Answer

C. 13

Answer 2

C, since both triangles are similar （angle a is shared, angle P and angle C are congruent, and Angle Q and Angle C are congruent from PQ and BC are parallel.

Then we can derive the equation for solving the similar polygons using ratios：

$\frac{6}{x} = \frac{18}{x + 26}$
by using cross multiplication we can make the equation like this:
$6x + 156 = 12x$
and we only have to solve for x which is:
$156 = 12x$
$x = 13$