Question

quadrilateral abcd is a rectangle, ae = b + 2, and de = 2b - 73. what is the value of b?

Explanation:

Step1: Use the property of rectangle's diagonals

In a rectangle, the diagonals are equal and bisect each other. So \(AE = DE\).

Step2: Set up the equation

Given \(AE=b + 2\) and \(DE=2b-73\), we have the equation \(b + 2=2b-73\).

Step3: Solve the equation

Subtract \(b\) from both sides: \(2=2b - 73-b\), which simplifies to \(2=b - 73\).
Add 73 to both sides: \(b=2 + 73\).

Answer:

\(b = 75\)