Question

520va v. geometry sem a geometry foundations of euclidean geometry point g lies between points f and h on fh. if the length of fh is 18 units, what is the value of x? 3 12 4 6

Explanation:

Step1: Set up length - relation equation

Since point G lies between F and H on $\overline{FH}$, we know that $FH = FG+GH$. Given $FG = 4x$, $GH = 2x$, and $FH = 18$, we have the equation $4x + 2x=18$.

Step2: Combine like - terms

Combining the left - hand side of the equation, $4x+2x$ gives $6x$. So the equation becomes $6x = 18$.

Step3: Solve for x

Divide both sides of the equation $6x = 18$ by 6. We get $x=\frac{18}{6}=3$.

Answer:

3