Question

given that ( a b c d ) is a rectangle with ( a o = 4 x - 3 ) and ( b o = 5 x - 10 ), what is the value of ( x )?
(1 point)
( \bigcirc x = -\frac{4}{3} )
( \bigcirc x = \frac{17}{6} )
( \bigcirc x = 7 )
( \bigcirc x = - 13 )

Explanation:

Step1: Use the property of rectangle diagonals

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

Step2: Set up the equation

Since \(AO = 4x - 3\) and \(BO = 5x - 10\), we have the equation \(4x - 3=5x - 10\).

Step3: Solve the equation for \(x\)

Subtract \(4x\) from both sides: \(-3=x - 10\).
Then add \(10\) to both sides: \(x=7\).

Answer:

\(x = 7\)