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 property of parallelogram diagonals

In a parallelogram, 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: \(26 = 2c\)
Divide by 2: \(c = 13\)

Step3: Find \(GK\)

Substitute \(c = 13\) into \(GK=c + 12\). So \(GK=13 + 12=25\)

Step4: Find \(GL\)

Since \(GL = 2GK\) (diagonals bisect each other), \(GL=2\times25 = 50\)

Answer:

\(50\)