Question

quadrilateral tuvw is a rectangle, vx = 10c + 19, and wx = 9c + 23. what is tv?

Explanation:

Step1: Use the property of rectangle diagonals

In a rectangle, the diagonals are equal and bisect each other. So \(VX = WX\).
\(10c + 19=9c + 23\)

Step2: Solve for \(c\)

Subtract \(9c\) from both sides: \(10c-9c+19 = 9c - 9c+23\), which gives \(c+19 = 23\).
Then subtract \(19\) from both sides: \(c+19 - 19=23 - 19\), so \(c = 4\).

Step3: Find \(VX\) or \(WX\)

Substitute \(c = 4\) into \(VX=10c + 19\): \(VX=10\times4+19=40 + 19=59\).
Since \(VX = WX\), the length of the diagonal \(VW=2VX\) (or \(2WX\)).

Step4: Calculate \(TV\)

In a rectangle, the diagonals are equal. So \(TV = VW\). \(TV = 2\times59 = 118\).

Answer:

\(118\)