Question

f is the midpoint of $overline{eg}$. if $ef = 10x$ and $fg = 8x + 10$, what is $ef?

simplify your answer and write it as a proper fraction, mixed number, or integer.

Explanation:

Step1: Use mid - point property

Since F is the mid - point of EG, then $EF = FG$. So we set up the equation $10x=8x + 10$.

Step2: Solve for x

Subtract $8x$ from both sides of the equation: $10x-8x=8x + 10-8x$. This simplifies to $2x=10$. Then divide both sides by 2: $x=\frac{10}{2}=5$.

Step3: Find EF

We know that $EF = 10x$. Substitute $x = 5$ into the expression for EF. So $EF=10\times5 = 50$.

Answer:

50