Question

if $overline{hk}congoverline{jk}$, $hi = 4w$, and $ij=w + 6$, what is the value of $w$?

Explanation:

Step1: Apply congruent - segment property

Since $\overline{HK}\cong\overline{JK}$, and $KI$ is perpendicular to $HJ$, by the property of the perpendicular bisector of a segment (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 $4w=w + 6$.

Step3: Solve the equation for $w$

Subtract $w$ from both sides: $4w−w=w + 6−w$, which simplifies to $3w=6$. Then divide both sides by 3: $\frac{3w}{3}=\frac{6}{3}$, so $w = 2$.

Answer:

$2$