Question

if \\(\overline{hk} \cong \overline{jk}\\), \\(hi = 3b\\), and \\(ij = b + 50\\), what is the value of \\(b\\)?
\\(b = \square\\)

Explanation:

Step1: Identify the property

Since \( \overline{HK} \cong \overline{JK} \) and \( KI \) is perpendicular to \( JH \), by the perpendicular bisector theorem, \( KI \) bisects \( JH \) and \( HI = IJ \).

Step2: Set up the equation

Given \( HI = 3b \) and \( IJ = b + 50 \), set them equal: \( 3b = b + 50 \).

Step3: Solve for \( b \)

Subtract \( b \) from both sides: \( 3b - b = 50 \), which simplifies to \( 2b = 50 \). Then divide by 2: \( b = \frac{50}{2} = 25 \).

Answer:

25