Question

for what value of x is the parallelogram a rectangle? the parallelogram is a rectangle when x = \boxed{}. (type a whole number.)

Explanation:

Step1: Recall rectangle property

In a rectangle, the diagonals are equal and bisect each other, so the angles formed by the diagonal and a side are equal. Thus, \(4x - 6 = 3x + 7\).

Step2: Solve for x

Subtract \(3x\) from both sides: \(4x - 3x - 6 = 3x - 3x + 7\)
Simplify: \(x - 6 = 7\)
Add 6 to both sides: \(x - 6 + 6 = 7 + 6\)
Simplify: \(x = 13\)

Answer:

13