Question

For the rectangle shown, AO = 9x-1 and OD = 6x+17. Find AC.



AC =

Answer 1

To solve for AC in the rectangle, we need to understand the relationships between the sides of the rectangle. In a rectangle, opposite sides are equal in length.

Given:
- AO = 9x - 1
- OD = 6x + 17

Since AO is vertical and OD is horizontal, we can say that AO is equal to OD because they are opposite sides of the rectangle.

So, we set up the equation:
\[
9x - 1 = 6x + 17
\]

Now we can solve for \( x \):

1. Subtract \( 6x \) from both sides:
\[
9x - 6x - 1 = 17
\]
\[
3x - 1 = 17
\]

2. Add 1 to both sides:
\[
3x = 18
\]

3. Divide by 3:
\[
x = 6
\]

Now that we have \( x \), we can substitute it back into either expression for AO or OD to find the length of AC (which is equal to AO):

Using AO:
\[
AO = 9x - 1 = 9(6) - 1 = 54 - 1 = 53
\]

Therefore, the length of AC is:
\[
\text{AC} = 53
\]

So, the final answer is:
\[
AC = 53
\]