Question

if $overline{gh}congoverline{gj}$, $hi = 3p$, and $ij=p + 56$, what is the value of $p$?

Explanation:

Step1: Apply congruence property

Since $\overline{GH}\cong\overline{GJ}$, by the property of congruent - sided triangles and the perpendicular bisector theorem (if a point is on the perpendicular bisector of a segment, it is equidistant from the endpoints of the segment), we know that $HI = IJ$.

Step2: Set up the equation

Set up the equation based on the given expressions for $HI$ and $IJ$. We have $3p=p + 56$.

Step3: Solve the equation for $p$

Subtract $p$ from both sides of the equation: $3p−p=p + 56−p$. This simplifies to $2p=56$. Then divide both sides by 2: $\frac{2p}{2}=\frac{56}{2}$, so $p = 28$.

Answer:

$28$