Question

qrst is a parallelogram.
find the measure of st.
enter the correct value in the box.

Explanation:

Step1: Recall parallelogram property

In a parallelogram, opposite sides are equal. So, \(QR = TS\).
Given \(QR = 6x - 9\) and \(TS = 4x + 3\), we set them equal: \(6x - 9 = 4x + 3\).

Step2: Solve for \(x\)

Subtract \(4x\) from both sides: \(6x - 4x - 9 = 4x - 4x + 3\)
\(2x - 9 = 3\)
Add 9 to both sides: \(2x - 9 + 9 = 3 + 9\)
\(2x = 12\)
Divide by 2: \(x = \frac{12}{2} = 6\).

Step3: Find \(ST\)

Substitute \(x = 6\) into \(ST = 4x + 3\):
\(ST = 4(6) + 3 = 24 + 3 = 27\).

Answer:

27