Question

given that the quadrilateral is a parallelogram,
\\( \overline { q s } = 4 x - 3 \\) and \\( \overline { r t } = 2 x + 11 \\), what is \\( \overline { r t } \\)?
\\( \overline { r t } = \\)

Explanation:

Step1: Use the property of parallelogram

In a parallelogram, opposite sides are equal. So, $\overline{QS}=\overline{RT}$.
Given $\overline{QS} = 4x - 3$ and $\overline{RT}=2x + 11$, we set up the equation $4x-3=2x + 11$.

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides:
$$4x-2x-3=2x-2x + 11$$
$$2x-3=11$$
Add \(3\) to both sides:
$$2x-3 + 3=11+ 3$$
$$2x=14$$
Divide both sides by \(2\):
$$x=\frac{14}{2}=7$$

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

Substitute \(x = 7\) into the expression for \(\overline{RT}\) (\(\overline{RT}=2x + 11\)):
$$\overline{RT}=2\times7+11=14 + 11=25$$

Answer:

\(25\)