Question

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

Explanation:

Step1: Use similarity of triangles

Since $\overline{YZ}\parallel\overline{WX}$, $\triangle VYZ\sim\triangle VWX$. Then the ratios of corresponding - sides are equal. That is, $\frac{VY}{VW}=\frac{VZ}{VX}$.
We know that $VY = 25$, $VW=25 + 5=30$, $VZ=x$, and $VX=x + 7$. So, $\frac{25}{30}=\frac{x}{x + 7}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{25}{30}=\frac{x}{x + 7}$ gives us $25(x + 7)=30x$.
Expand the left - hand side: $25x+175 = 30x$.

Step3: Solve for x

Subtract $25x$ from both sides of the equation $25x+175 = 30x$. We get $175=30x−25x$.
Combining like terms, $5x = 175$.
Divide both sides by 5: $x=\frac{175}{5}=35$.

Answer:

$35$