Question

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



(1 point)
AC =

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Answer 1

To solve this problem, we first need to understand that in a rectangle, opposite sides are equal in length. Therefore, the length AO will be equal to the length OD.

We can set up the equation based on the information provided:

\[
AO = OD
\]

Substituting the expressions given:

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

Next, we 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, we will use this value of \(x\) to find the lengths of AO and OD.

Calculating \(AO\):

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

Calculating \(OD\):

\[
OD = 6x + 17
\]
\[
OD = 6(6) + 17
\]
\[
OD = 36 + 17
\]
\[
OD = 53
\]

Since \(AC\) is equal to \(AO\) or \(OD\) in a rectangle, we find:

\[
AC = 53
\]

Thus, the answer is:

\[
AC = 53
\]