Consider the parallelogram ABCD. If AC = 2x + 15 and BD = 5 - 12, what does the value of a need to be so that the parallelogram is a rectangle?
(1 point)
To determine the value of a that makes the parallelogram a rectangle, we need to find the condition that makes the diagonals of the parallelogram equal. In a rectangle, the diagonals are always equal.
Since ABCD is a parallelogram, opposite sides are equal. Therefore, AC = BD.
Given that AC = 2x + 15 and BD = 5 - 12, we can set these two expressions equal:
2x + 15 = 5 - 12
Simplifying the equation:
2x + 15 = -7
Subtracting 15 from both sides:
2x = -7 - 15
2x = -22
Dividing both sides by 2:
x = -22/2
x = -11
Therefore, the value of a needs to be -11 for the parallelogram ABCD to be a rectangle.