Question

in the diagram below, $overline{yz}paralleloverline{wx}$. find the value of $k$. the diagram is not drawn to scale.

Explanation:

Step1: Apply similar - triangle property

Since $\overline{YZ}\parallel\overline{WX}$, then $\triangle VYZ\sim\triangle VWX$. The ratios of corresponding sides of similar triangles are equal. That is, $\frac{VY}{VW}=\frac{VZ}{VX}$. We know that $VY = 6$, $VW=6 + 10=16$, $VZ = 18$, and $VX=18 + k$.
So, $\frac{6}{16}=\frac{18}{18 + k}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{6}{16}=\frac{18}{18 + k}$ gives us $6(18 + k)=16\times18$.
Expand the left - hand side: $108+6k = 288$.

Step3: Solve for $k$

Subtract 108 from both sides of the equation $108+6k = 288$:
$6k=288 - 108$.
$6k = 180$.
Divide both sides by 6: $k=\frac{180}{6}=30$.

Answer:

$30$