To determine the value of \( x \) that proves parallelogram ABCD is a rectangle, we need to use the information given about the diagonals.
Since the diagonals of a rectangle are congruent, we can set the lengths of diagonals AC and DO equal to each other:
\[ AC = DO \]
From the problem, we have: \[ AC = 48 \] \[ DO = 7x + 3 \]
Setting these equal gives us the equation: \[ 48 = 7x + 3 \]
To solve for \( x \), we will first subtract 3 from both sides: \[ 48 - 3 = 7x \] \[ 45 = 7x \]
Next, we divide both sides by 7: \[ x = \frac{45}{7} \]
This does not appear to be one of the provided answer choices. Let's check our steps again.
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Confirm that we have set the equation correctly:
- \( AC = 48 \)
- \( DO = 7x + 3 \)
- Therefore, \( 48 = 7x + 3 \) is indeed correct.
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Solve:
- \( 48 - 3 = 7x \) → \( 45 = 7x \)
- \( x = \frac{45}{7} \) does not correspond to the provided options.
It seems there might be a misunderstanding in the components provided or expected. Please verify against the problem resource or context.
From literal interpretation of the length of diagonals being equal, check if a rounded value closer to standard integers is meant; typically in setups, integers come through multiple-choice frameworks. Assuming the context implies otherwise based on acceptable values, simply evaluating a guess based on rounding won't deliver an answer fitting classical expectations of whole integer variables like \( x=6 \) being closest would rather be the reassessment dealing contextually.
However, among the answers presented none directly pass unless we'd round towards allowance or decision-making points based on integerization on understanding premises, or confirm if the actual theoretical expectation diverges here on \( x \).
If you fancy backtracking or errors in the construction, values are recomposed accordingly without severe deviation, or appropriateness transformed statistically. Otherwise, 48 as your diagonal is targeting sole representation against 45 integer pegging again simply isn't typical or allowed through standard integer sets creating divergent outputs on paraboloid provision techniques.
1 answer