Question

given that the quadrilateral is a parallelogram,
\\( \overline { q s } = 5 x - 1 \\) and \\( \overline { r t } = 2 x + 20 \\), what is \\( \overline { r t } \\)?

\\( \overline { r t } = \\)______

Explanation:

Step1: Use the property of parallelogram

In a parallelogram, opposite sides are equal. So, \( \overline{QS}=\overline{RT} \).
$$5x - 1=2x + 20$$

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides:
$$5x-2x - 1=2x-2x + 20$$
$$3x-1 = 20$$
Add \(1\) to both sides:
$$3x-1 + 1=20 + 1$$
$$3x=21$$
Divide both sides by \(3\):
$$x=\frac{21}{3}=7$$

Step3: Find the length of \( \overline{RT} \)

Substitute \(x = 7\) into the expression for \( \overline{RT}\) (\( \overline{RT}=2x + 20\)):
$$\overline{RT}=2\times7+20$$
$$=14 + 20$$
$$=34$$

Answer:

\(34\)