Question

if hi = ij = 60, hk = 2v, and jk = v + 20, what is hk?

Explanation:

Step1: Apply property of perpendicular bisector

Since $HI = IJ$ and $IK\perp HJ$, then $IK$ is the perpendicular - bisector of $HJ$, so $HK=JK$.

Step2: Set up the equation

Set $2v=v + 20$.

Step3: Solve the equation for $v$

Subtract $v$ from both sides: $2v−v=v + 20−v$, which gives $v = 20$.

Step4: Find the value of $HK$

Since $HK = 2v$ and $v = 20$, then $HK=2\times20=40$.

Answer:

$40$