Question

in the diagram below, $overline{fg}$ is parallel to $overline{cd}$. solve for $x$. round your answer to the nearest tenth if necessary.

Explanation:

Step1: Apply similar - triangle property

Since $\overline{FG}\parallel\overline{CD}$, then $\triangle EFG\sim\triangle ECD$. The ratios of corresponding sides of similar triangles are equal. So, $\frac{EF}{EC}=\frac{EG}{ED}$. We know that $EF = 10$, $EG = 12.5$, $ED=12.5 + 7.5=20$, and $EC=10 + x$.
So, $\frac{10}{10 + x}=\frac{12.5}{20}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{10}{10 + x}=\frac{12.5}{20}$ gives us $10\times20=12.5\times(10 + x)$.
$200 = 125+12.5x$.

Step3: Solve for $x$

Subtract 125 from both sides: $200−125 = 12.5x$.
$75 = 12.5x$.
Then divide both sides by 12.5: $x=\frac{75}{12.5}=6$.

Answer:

$6$