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

B
C
9x-1 г
O
6x + 17
A
(1 point)
AC =
D

1 answer

To find \( AC \) in the rectangle, we need to use the properties of a rectangle and the fact that opposite sides are equal in length.

In this rectangle:

  • Side \( AO \) has a length of \( 9x - 1 \).
  • Side \( OD \) has a length of \( 6x + 17 \).

Since \( AO \) and \( OD \) are opposite sides of the rectangle, we can set them equal to each other:

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

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 \( x = 6 \), we can find the lengths of \( AO \) and \( OD \):

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

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

Since both sides are equal, this confirms our calculations are correct.

Now, to find \( AC \), we look at the other pair of opposite sides of the rectangle (which are equal):

Since \( B \) is opposite to \( D \), \( AC \) will also equal the same length as \( AO \) and \( OD \):

\[ AC = AO = 53 \]

Thus, the final answer for \( AC \) is:

\[ \boxed{53} \]