Question

$\overline{wx} \parallel \overline{tv}$. find $vw$.

Explanation:

Step1: Define proportional segments

Since $\overline{WX} \parallel \overline{TV}$, by the Triangle Proportionality Theorem, the segments created on the sides of $\triangle UWX$ are proportional:
$\frac{UV}{VW} = \frac{UT}{TX}$

Step2: Assign known values

Let $VW = x$. We know $UV = 84$, $UT = 42$, $TX = 17$. Substitute into the proportion:
$\frac{84}{x} = \frac{42}{17}$

Step3: Cross-multiply to solve for $x$

Cross-multiply to isolate $x$:
$42x = 84 \times 17$

Step4: Calculate and simplify

First compute $84 \times 17 = 1428$, then solve for $x$:
$x = \frac{1428}{42} = 34$

Answer:

34