Question

if $overline{eh}congoverline{gh}$, $ef = 3t$, and $fg=t + 6$, what is the value of $t$?

Explanation:

Step1: Use property of congruent segments

Since $\overline{EH}\cong\overline{GH}$ and the line through $F$ is perpendicular to $\overline{EH}$ and $\overline{GH}$, by the property of the perpendicular - bisector of a segment (a point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment), we have $EF = FG$.

Step2: Set up the equation

Set up the equation $3t=t + 6$.

Step3: Solve the equation

Subtract $t$ from both sides: $3t-t=t + 6-t$, which simplifies to $2t=6$. Then divide both sides by 2: $\frac{2t}{2}=\frac{6}{2}$, so $t = 3$.

Answer:

$3$