In parallelogram ABCD, the diagonals are congruent if it is a rectangle. Given that \( AC = 48 \) and the length of diagonal \( DO = 7x + 3 \), we need to set these equal to each other since, in a rectangle, the diagonals are equal.
So, we set up the equation:
\[ 7x + 3 = 48 \]
To solve for \( x \), first subtract 3 from both sides:
\[ 7x = 48 - 3 \] \[ 7x = 45 \]
Now, divide both sides by 7:
\[ x = \frac{45}{7} \] \[ x = 6.4286 \text{ (approximately)} \]
This value does not seem to correspond with your provided options of \( 4, 8, 6, \) or \( 3 \). Let’s check again, using each of the provided choices to see if any yield a diagonal length of 48.
- If \( x = 4 \): \[ DO = 7(4) + 3 = 28 + 3 = 31 \]
- If \( x = 8 \): \[ DO = 7(8) + 3 = 56 + 3 = 59 \]
- If \( x = 6 \): \[ DO = 7(6) + 3 = 42 + 3 = 45 \]
- If \( x = 3 \): \[ DO = 7(3) + 3 = 21 + 3 = 24 \]
Since none of the provided values satisfy the condition \( DO = AC = 48 \), it seems there may have been a misunderstanding or error in the question regarding the length of diagonal \( DO \).
However, based on the congruency of the diagonals, the value of \( x \) that gives \( DO \) equal to \( 48 \) from \( AC \) cannot be found in the given options. If \( AC \) is indeed \( 48 \), there appears to be no valid choice provided. Please verify the values or the question for accuracy.