Question

use the image to answer the question
given the rectangle abcd as shown, find ac if ao = 9x - 1 and do = 6x + 17.
(1 point)
ac =

Explanation:

Step1: Use the property of rectangle diagonals

In a rectangle, the diagonals are equal and bisect each other. So \(AO = DO\).
\(9x - 1=6x + 17\)

Step2: Solve for \(x\)

Subtract \(6x\) from both sides: \(9x-6x - 1=6x-6x + 17\), \(3x-1 = 17\).
Add \(1\) to both sides: \(3x-1 + 1=17 + 1\), \(3x=18\).
Divide both sides by \(3\): \(x=\frac{18}{3}=6\).

Step3: Find \(AO\)

Substitute \(x = 6\) into \(AO=9x - 1\), \(AO=9\times6-1=54 - 1=53\).

Step4: Calculate \(AC\)

Since \(AC = 2AO\) (diagonals bisect each other), \(AC=2\times56 = 112\).

Answer:

\(112\)