Question

in δhik, hj is a median.
what is the length of (overline{hi})?
a 12
b 35
c 13
d 63

Explanation:

Step1: Recall median property

Since $\overline{HJ}$ is a median, $KJ = JI$. So, $x=3x - 12$.

Step2: Solve for $x$

Subtract $x$ from both sides: $0 = 3x-12 - x$, which simplifies to $0 = 2x-12$. Then add 12 to both sides: $12 = 2x$. Divide by 2, we get $x = 6$.

Step3: Find length of $\overline{HI}$

Substitute $x = 6$ into the expression for $HI=2x + 1$. So, $HI=2\times6+1=12 + 1=13$.

Answer:

C. 13