Question

given that the quadrilateral is a parallelogram,
\\( \overline { q s } = 5 x - 2 \\) and \\( \overline { r t } = 2 x + 13 \\), what is \\( \overline { r t } \\)?
\\( \overline { r t } = \\)
question 15
1 pts

Explanation:

Step1: Use the property of parallelogram

In a parallelogram, opposite sides are equal. So, \( \overline{QS}=\overline{RT}\).
Given \( \overline{QS} = 5x - 2\) and \( \overline{RT}=2x + 13\), we set up the equation \(5x-2=2x + 13\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(5x-2x-2=2x-2x + 13\), which simplifies to \(3x-2=13\).
Add \(2\) to both sides: \(3x-2 + 2=13+ 2\), so \(3x=15\).
Divide both sides by \(3\): \(x=\frac{15}{3}=5\).

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

Substitute \(x = 5\) into the expression for \( \overline{RT}\).
\( \overline{RT}=2x+13\), so \( \overline{RT}=2\times5+13\).
\( \overline{RT}=10 + 13=23\).

Answer:

\(23\)