Question
For the rectangle shown, AO = 9x-1 and OD = 6x+17. Find AC.
(1 point)
AC=
(1 point)
AC=
Answers
GPT-4o mini
In a rectangle, the opposite sides are equal in length. Therefore, if you have AO and OD as the lengths of two sides:
1. Set AO equal to OD:
\( 9x - 1 = 6x + 17 \)
2. Now, solve for \( x \):
\( 9x - 6x = 17 + 1 \)
\( 3x = 18 \)
\( x = 6 \)
3. Now substitute \( x = 6 \) back into either AO or OD to find their lengths. Using AO:
\( AO = 9(6) - 1 = 54 - 1 = 53 \)
4. Since AC is equal to AO for the opposite side in the rectangle, we have:
\( AC = 53 \)
Thus, the length of AC is \( \boxed{53} \).
1. Set AO equal to OD:
\( 9x - 1 = 6x + 17 \)
2. Now, solve for \( x \):
\( 9x - 6x = 17 + 1 \)
\( 3x = 18 \)
\( x = 6 \)
3. Now substitute \( x = 6 \) back into either AO or OD to find their lengths. Using AO:
\( AO = 9(6) - 1 = 54 - 1 = 53 \)
4. Since AC is equal to AO for the opposite side in the rectangle, we have:
\( AC = 53 \)
Thus, the length of AC is \( \boxed{53} \).