Question

finding a diagonal measure
in parallelogram hgjl, hk = c - 7, jk = 3c - 33, and gk = c + 12. what is the length of segment gl?
gl = units

Explanation:

Step1: Recall parallelogram diagonal property

In a parallelogram, the diagonals bisect each other. So, \( HK = JK \).
Given \( HK = c - 7 \) and \( JK = 3c - 33 \), we set up the equation:
\( c - 7 = 3c - 33 \)

Step2: Solve for \( c \)

Subtract \( c \) from both sides:
\( -7 = 2c - 33 \)
Add 33 to both sides:
\( 26 = 2c \)
Divide by 2:
\( c = 13 \)

Step3: Find length of \( GK \)

Given \( GK = c + 12 \), substitute \( c = 13 \):
\( GK = 13 + 12 = 25 \)

Step4: Find length of \( GL \)

In a parallelogram, \( GL = 2 \times GK \) (since diagonals bisect each other, so \( GL = GK + LK \) and \( GK = LK \)):
\( GL = 2 \times 25 = 50 \)

Answer:

50