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: Use parallelogram diagonal property

In a parallelogram, diagonals bisect each other, so $HK = JK$.
$c - 7 = 3c - 33$

Step2: Solve for $c$

Rearrange to isolate $c$:
$33 - 7 = 3c - c$
$26 = 2c$
$c = \frac{26}{2} = 13$

Step3: Find length of GK

Substitute $c=13$ into $GK = c + 12$:
$GK = 13 + 12 = 25$

Step4: Calculate length of GL

Diagonals bisect, so $GL = 2 \times GK$:
$GL = 2 \times 25 = 50$

Answer:

50 units