Question
Because congruent diagonals prove that a parallelogram is a rectangle, what value of x proves that parallelogram ABCD is a rectangle if AC = 48 and DO = 7x + 3?
a. x = 8
b. x = 4
c. x = 6
d. x = 3
a. x = 8
b. x = 4
c. x = 6
d. x = 3
Answers
GPT-4o mini
In a parallelogram, if the diagonals are congruent (equal in length), then it is a rectangle. Given that the length of diagonal \( AC \) is 48 and the length of diagonal \( DO \) is given as \( 7x + 3 \), we can set up the equation:
\[
7x + 3 = 48
\]
Now, solve for \( x \):
1. Subtract 3 from both sides:
\[
7x = 48 - 3
\]
\[
7x = 45
\]
2. Now, divide both sides by 7:
\[
x = \frac{45}{7}
\]
This results in:
\[
x = 6.42857 \ldots
\]
None of the provided options \( a (8), b (4), c (6), d (3) \) satisfy this equation exactly. Therefore, double-checking the problem statement and numbers is necessary because the given values do not lead to any of the provided answers being true.
If you consider reasoning simply if \( 7x + 3 \) must also equal 48 in order for the diagonals to be congruent. You might want to double-check for possible misprints or ensure the parameters match your calculation.
\[
7x + 3 = 48
\]
Now, solve for \( x \):
1. Subtract 3 from both sides:
\[
7x = 48 - 3
\]
\[
7x = 45
\]
2. Now, divide both sides by 7:
\[
x = \frac{45}{7}
\]
This results in:
\[
x = 6.42857 \ldots
\]
None of the provided options \( a (8), b (4), c (6), d (3) \) satisfy this equation exactly. Therefore, double-checking the problem statement and numbers is necessary because the given values do not lead to any of the provided answers being true.
If you consider reasoning simply if \( 7x + 3 \) must also equal 48 in order for the diagonals to be congruent. You might want to double-check for possible misprints or ensure the parameters match your calculation.