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. options: 6, 25, 38, 50

Explanation:

Step1: Use property of parallelogram diagonals

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

Step2: Solve for c

Subtract c from both sides: $- 7 = 2c-33$.
Add 33 to both sides: $2c=26$, then $c = 13$.

Step3: Find length of GK

Substitute $c = 13$ into the expression for $GK$. $GK=c + 12=13 + 12=25$.

Step4: Find length of GL

Since the diagonals bisect each other, $GL = 2\times GK$. So $GL=2\times25 = 50$.

Answer:

50