To determine the value of \( x \) that proves parallelogram ABCD is a rectangle using the condition that congruent diagonals indicate a rectangle, we need to equate the diagonals \( AC \) and \( DO \).
Given:
- \( AC = 48 \)
- \( DO = 7x + 3 \)
Since congruent diagonals imply that the diagonals are equal in length for parallelogram ABCD to be a rectangle, we can set up the equation:
\[ AC = DO \]
Substituting the given values:
\[ 48 = 7x + 3 \]
Now, we will solve for \( x \):
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Subtract 3 from both sides: \[ 48 - 3 = 7x \] \[ 45 = 7x \]
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Divide both sides by 7: \[ x = \frac{45}{7} \approx 6.43 \]
Since \( x \) must be one of the provided options (6, 3, 8, or 4), we can conclude that there may be a misunderstanding in the problem's constraints since none of the options represent \(\frac{45}{7}\).
If we factor in the possibility of re-evaluating the given responses or confirming the original lengths e.g. checking \( AC \) or \( DO \) again, at least based on this equation, \( x \approx 6.43\) does not fit anyone of the options therefore no correct answer among provided options would be applicable here.
However, if the equations originally assumed any simplified integer forms, unfortunately, from this derived fact, none can truly match provided numeric choices. Please verify the question or values once again.
1 answer