Question

in the diagram below, $overline{fg}$ is parallel to $overline{cd}$. solve for $x$. round your answer to the nearest tenth if necessary. side splitter: if a line intersects two sides of a triangle and is parallel to the third, it divides the 2 sides proportionally.

Explanation:

Step1: Apply side - splitter theorem

Since $\overline{FG}\parallel\overline{CD}$, we have the proportion $\frac{EF}{FC}=\frac{EG}{GD}$. Here, $EF = 10$, $EG=12.5$, $GD = 7.5$, and $FC=x$. So the proportion is $\frac{10}{x}=\frac{12.5}{7.5}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{10}{x}=\frac{12.5}{7.5}$ gives us $12.5x=10\times7.5$.

Step3: Solve for $x$

First, calculate $10\times7.5 = 75$. Then, $x=\frac{75}{12.5}=6$.

Answer:

$6$