Question

if ( rt = 3b - 71 ) and ( rv = 2b - 40 ), find ( rv ) in rectangle ( stuv ).

Explanation:

Step1: Use the property of rectangle diagonals

In a rectangle, the diagonals are equal and bisect each other. So \(RT = RV\).
\(3b - 71=2b - 40\)

Step2: Solve for \(b\)

Subtract \(2b\) from both sides: \(3b-2b - 71=2b-2b - 40\), which gives \(b - 71=- 40\).
Add \(71\) to both sides: \(b-71 + 71=-40 + 71\), so \(b = 31\).

Step3: Find \(RV\)

Substitute \(b = 31\) into \(RV=2b - 40\).
\(RV=2\times31-40\)
\(RV = 62-40\)

Answer:

\(22\)