Answer
$x = 10$
The scale factor for $\triangle WLJ:\triangle QBV$ is $\frac{2}{1}$.
Work Step by Step
In similar triangles, corresponding sides are proportional. In $\triangle WLJ$ and $\triangle QBV$, we have the following corresponding sides:
$WL ≅ QB$
$LJ ≅ BV$
$JW ≅ VQ$
Let's use what we know and put this given information into a proportion:
$\frac{WL}{BV} = \frac{JW}{VQ}$
Now we plug in values for the sides:
$\frac{x}{5} = \frac{x + 6}{8}$
Cross multiply to get rid of the fraction:
$5(x + 6) = 8x$
Distribute on the left side of the equation:
$5x + 30 = 8x$
Subtract $5x$ from each side of the equation to move variables to one side of the equation:
$3x = 30$
Divide both sides by $3$ to solve for $x$:
$x = 10$
To find the scale factor, locate corresponding sides on the two triangles and put them into a ratio:
$\frac{WL}{BV} = \frac{x}{5}$
Replace $x$ with $10$:
$\frac{WL}{BV} = \frac{10}{5}$
Divide both the numerator and denominator by their greatest common factor, $5$:
$\frac{WL}{BV} = \frac{2}{1}$
The scale factor for $\triangle WLJ:\triangle QBV$ is $\frac{2}{1}$.
