Question

if ( rt = 3b - 86 ) and ( rv = b ), find ( rt ) in parallelogram ( stuv ).

Explanation:

Step1: Use property of parallelogram diagonals

In a parallelogram, diagonals bisect each other. So \(RT = RV\).

Step2: Set up equation

Given \(RT = 3b - 86\) and \(RV = b\), we set \(3b - 86=b\).

Step3: Solve for \(b\)

Subtract \(b\) from both sides: \(3b - b-86=b - b\), which gives \(2b-86 = 0\). Then add \(86\) to both sides: \(2b-86 + 86=86\), so \(2b=86\). Divide both sides by \(2\): \(b=\frac{86}{2}=43\).

Step4: Find \(RT\)

Since \(RT = 3b - 86\) and \(b = 43\), substitute \(b\) into the formula: \(RT=3\times43-86\). First, calculate \(3\times43 = 129\). Then \(129-86 = 43\).

Answer:

\(43\)