Question

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

Answer 1

In a rectangle, opposite sides are equal. Therefore, we can set AO equal to OD:

\[
AO = OD
\]

Substituting the given expressions:

\[
9x - 1 = 6x + 17
\]

Now, we will solve for \(x\):

1. Subtract \(6x\) from both sides:

\[
9x - 6x - 1 = 17
\]
\[
3x - 1 = 17
\]

2. Add 1 to both sides:

\[
3x = 17 + 1
\]
\[
3x = 18
\]

3. Divide by 3:

\[
x = \frac{18}{3} = 6
\]

Now that we have the value of \(x\), we can find \(AO\) (and \(OD\) since they are equal).

Substituting \(x = 6\) into \(AO\):

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

Now, we can find \(AC\).

In a rectangle, if AO is one side and OC (which is equal to AO) is the other side, and if AC is the length across from AO to side OD, then AC is equal to the length of AO, which is:

\[
AC = AO = 53
\]

Thus, the final answer is:

\[
\boxed{53}
\]