Therefore, the value of x that proves the parallelogram ABCD is a rectangle is x = 19. Option D
How to determine the value of x
To determine the value of x that proves the parallelogram ABCD is a rectangle, use the properties of diagonals in a rectangle.
In a rectangle, the diagonals are congruent and bisect each other. This means that if ABCD is a rectangle, then AE = CE and BE = DE.
Given that ED = 7x + 21, we can set it equal to BE:
ED = BE
7x + 21 = BE
We also know that AC = 154, which is the same as BE:
AC = BE
154 = BE
Setting the two expressions for BE equal to each other, we have:
7x + 21 = 154
Now, solve for x:
7x + 21 = 154
Subtract 21 from both sides:
7x = 154 - 21
7x = 133
Divide both sides by 7:
x = 133 / 7
x = 19
Therefore, the value of x that proves the parallelogram ABCD is a rectangle is x = 19.
The correct answer is (d) 19.