Question

1. find the value of x. rz = 30 sw = 5x - 20

Explanation:

Step1: Recall property of rectangle

In a rectangle, the diagonals are equal and bisect each other. So \(RZ=\frac{1}{2}RW\) and \(SW = RW\), then \(SW = 2RZ\).

Step2: Set up equation

Given \(RZ = 30\) and \(SW=5x - 20\), and \(SW = 2RZ\), we substitute the values into the equation: \(5x-20=2\times30\).

Step3: Solve the equation

First, simplify the right - hand side: \(5x-20 = 60\). Then add 20 to both sides: \(5x=60 + 20\), so \(5x=80\). Divide both sides by 5: \(x=\frac{80}{5}=16\).

Answer:

16