Question

in shk, (overline{hj}) is a median.
what is the length of (overline{hk})?

Explanation:

Step1: Use the property of median

Since \( \overline{HJ} \) is a median of \( \triangle HIK \), it divides \( \overline{IK} \) into two equal parts. So \( 15x + 1=13x + 3 \).

Step2: Solve the equation for \( x \)

Subtract \( 13x \) from both sides: \( 15x-13x + 1=13x-13x + 3 \), which gives \( 2x+1 = 3 \).
Subtract \( 1 \) from both sides: \( 2x+1 - 1=3 - 1 \), so \( 2x=2 \).
Divide both sides by \( 2 \): \( x = 1 \).

Step3: Find the length of \( \overline{HK} \)

\( HK=(15x + 1)+(13x + 3) \). Substitute \( x = 1 \) into the expression:
\( HK=(15\times1 + 1)+(13\times1 + 3)=16 + 16=32 \).

Answer:

C. 32