Question

if fg = gh = 23, ef = 3p - 17, and eh = p + 7, what is ef?

Explanation:

Step1: Use the property of perpendicular bisector

Since $FG = GH$ and $GE\perp FH$, then $EF=EH$ (Perpendicular - bisector theorem).
So, we set up the equation $3p - 17=p + 7$.

Step2: Solve the equation for $p$

Subtract $p$ from both sides: $3p-p-17=p - p+7$, which simplifies to $2p-17 = 7$.
Add 17 to both sides: $2p-17 + 17=7 + 17$, getting $2p=24$.
Divide both sides by 2: $\frac{2p}{2}=\frac{24}{2}$, so $p = 12$.

Step3: Find the value of $EF$

Substitute $p = 12$ into the expression for $EF$.
$EF=3p-17=3\times12-17$.
$EF = 36-17$.
$EF = 19$.

Answer:

$19$