Question

given that quadrilateral ( abcd ) is a rectangle with ( ac = 7x ) and ( bd = 2x + 5 ), find the value of ( x ).

Explanation:

Step1: Use the property of rectangle diagonals

In a rectangle, the diagonals are equal. So \(AC = BD\).
Given \(AC = 7x\) and \(BD=2x + 5\), we set up the equation \(7x=2x + 5\).

Step2: Solve the equation for \(x\)

Subtract \(2x\) from both sides of the equation:
\(7x-2x=2x + 5-2x\)
\(5x=5\)
Divide both sides by \(5\):
\(x=\frac{5}{5}=1\)

Answer:

\(1\)