Question

find vw in rectangle tuvw.

Explanation:

Step1: Use the property of rectangle

In a rectangle, opposite sides are equal. So \(TU = VW\) and \(UV = TW\). Here we have \(TU=6c - 25\) and \(VW = 10c-69\). Set up the equation \(6c-25=10c - 69\).

Step2: Solve the equation for \(c\)

Subtract \(6c\) from both sides: \(-25 = 4c-69\).
Add \(69\) to both sides: \(44=4c\).
Divide both sides by \(4\): \(c = 11\).

Step3: Find the length of \(VW\)

Substitute \(c = 11\) into the expression for \(VW\) (\(VW=10c - 69\)).
\(VW=10\times11-69\).
\(VW = 110 - 69\).
\(VW=41\).

Answer:

\(41\)