Question

what is the value of z?
$z = \square$
(the figure shows triangle jik with jk = ji, jh is perpendicular to ik, ih = $9z$, hk = $z+48$)

Explanation:

Step1: Identify congruent segments

$JI = JK$ (marked congruent)

Step2: Use perpendicular bisector theorem

Since $JH \perp IK$ and $JI=JK$, $JH$ bisects $IK$, so $IH = HK$.

Step3: Set up equation

$9z = z + 48$

Step4: Solve for z

Subtract $z$ from both sides: $9z - z = 48$
$8z = 48$
Divide by 8: $z = \frac{48}{8}$

Answer:

$6$