Question

the diagram below shows rectangle rwts with z as the intersection of the two diagonals.
rz = 2x + 5,
sw = 5x - 20
if rz = 2x + 5 and sw = 5x - 20, what is the value of x?

Explanation:

Step1: Use the property of rectangle diagonals

In a rectangle, the diagonals are equal and bisect each other. So \(SW = 2RZ\).

Step2: Substitute the given expressions

Substitute \(RZ=2x + 5\) and \(SW = 5x-20\) into \(SW = 2RZ\). We get \(5x-20=2(2x + 5)\).

Step3: Expand and solve the equation

Expand the right - hand side: \(5x-20 = 4x+10\).
Subtract \(4x\) from both sides: \(5x-4x-20=4x - 4x+10\), which simplifies to \(x-20 = 10\).
Add 20 to both sides: \(x-20 + 20=10+20\).

Answer:

\(30\)