Question

what is the length of fg , when m is the midpoint of fg ? f m g 3x - 4 5x - 26

Explanation:

Step1: Use mid - point property

Since $M$ is the mid - point of $FG$, then $FM = MG$. So we set up the equation $3x - 4=5x - 26$.

Step2: Solve the equation for $x$

Subtract $3x$ from both sides: $- 4 = 5x-3x - 26$, which simplifies to $-4 = 2x-26$.
Add 26 to both sides: $-4 + 26=2x$, so $22 = 2x$.
Divide both sides by 2: $x = 11$.

Step3: Find the length of $FG$

$FG=FM + MG=(3x - 4)+(5x - 26)=8x-30$.
Substitute $x = 11$ into the expression for $FG$: $8\times11-30=88 - 30=58$.

Answer:

58