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 - triangles property

Since $\overline{YZ}\parallel\overline{WX}$, then $\triangle VYZ\sim\triangle VWX$. For similar triangles, the ratios of corresponding sides are equal. That is, $\frac{VY}{VW}=\frac{VZ}{VX}$.

Step2: Calculate the lengths of the sides

We know that $VZ = 24$, $VX=24 + 12=36$, and $VY = 8$, $VW=8 + k$. Substituting these values into the proportion $\frac{VY}{VW}=\frac{VZ}{VX}$, we get $\frac{8}{8 + k}=\frac{24}{36}$.

Step3: Cross - multiply

Cross - multiplying the proportion $\frac{8}{8 + k}=\frac{24}{36}$ gives us $24\times(8 + k)=8\times36$.
Expanding the left - hand side: $192+24k = 288$.

Step4: Solve for $k$

Subtract 192 from both sides: $24k=288 - 192$.
$24k = 96$.
Divide both sides by 24: $k=\frac{96}{24}=4$.

Answer:

$4$