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 the property of parallelogram diagonals

In a parallelogram, the diagonals bisect each other. So \(HK = JK\).

$$c - 7=3c - 33$$

Step2: Solve the equation for \(c\)

Subtract \(c\) from both sides:

$$ - 7=2c - 33$$

Add \(33\) to both sides:

$$26 = 2c$$

Divide both sides by \(2\):

$$c = 13$$

Step3: Find the length of \(GK\)

Substitute \(c = 13\) into \(GK=c + 12\)

$$GK=13 + 12=25$$

Step4: Find the length of \(GL\)

Since \(GL = 2GK\) (diagonals bisect each other)

$$GL=2\times25 = 50$$

Answer:

\(50\)