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 the equation 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 \(3\):
$$x = 6$$

Step3: Find the length of \(AO\)

Substitute \(x = 6\) into \(AO=9x - 1\):
$$AO=9\times6-1=54 - 1=53$$

Step4: Calculate the length of \(AC\)

Since \(AC = 2AO\) (diagonals bisect each other in a rectangle)
$$AC=2\times53 = 106$$

Answer:

\(106\)