Question

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

Explanation:

Step1: Apply the property of perpendicular bisector

Since $HI = IJ$ and the line through $I$ is perpendicular to $HJ$ at $K$, then $HK=JK$ (perpendicular - bisector property of an isosceles triangle).

Step2: Set up the equation

Set $2v=v + 20$.

Step3: Solve the equation for $v$

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

Step4: Find the value of $HK$

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

Answer:

40