Question

1. if vw = 9x - 11 and su = 16x - 12, find wt.

Explanation:

Step1: Use the property of rectangle diagonals

In a rectangle, the diagonals are equal and bisect each other. So \(SU = 2VW\).
Given \(VW=9x - 11\) and \(SU = 16x-12\), we substitute into the equation \(16x-12=2(9x - 11)\).

Step2: Solve the equation for \(x\)

Expand the right - hand side: \(16x-12 = 18x-22\).
Move the \(x\) terms to one side and constants to the other side: \(22 - 12=18x-16x\).
Simplify: \(10 = 2x\), then \(x = 5\).

Step3: Find \(VW\)

Substitute \(x = 5\) into \(VW=9x - 11\), we get \(VW=9\times5-11=45 - 11=34\).

Step4: Find \(WT\)

Since \(WT = VW\) (diagonals bisect each other in a rectangle), so \(WT = 34\).

Answer:

\(34\)