Question

$overline{uy} parallel overline{vx}$. find $vw$.

Explanation:

Step1: Apply Basic Proportionality Theorem

Since $\overline{UY} \parallel \overline{VX}$, the sides of $\triangle WUY$ are proportional to the sides of $\triangle WVX$. So, $\frac{WV}{WU} = \frac{WX}{WY}$.
Let $VW = x$. Then $WU = x + 36$, and $WY = 40 + 20 = 60$, $WX = 20$.
The proportion becomes: $\frac{x}{x + 36} = \frac{20}{60}$

Step2: Simplify the proportion

Simplify $\frac{20}{60}$ to $\frac{1}{3}$, so:
$\frac{x}{x + 36} = \frac{1}{3}$
Cross-multiply: $3x = x + 36$

Step3: Solve for $x$

Subtract $x$ from both sides:
$3x - x = 36$
$2x = 36$
$x = \frac{36}{2} = 18$

Answer:

18