For which value of x is xyza a rectangle

Answer:
The required value of x for which XYZA is a rectangle : x = -1
Step-by-step explanation:
Let the diagonals of the rectangle XYZA meet at point C
Since, The diagonal of rectangle bisect each other
⇒ AY = 2 × AC
⇒ AY = 2 × (5x - 5)
⇒ AY = 10x - 10
Also, XZ = 2 × CZ
⇒ XZ = 2 × (3x + 3)
⇒ XZ = 6x + 6
Now, Diagonals of rectangle are congruent to each other
⇒ AY = CZ
⇒ 10x + 10 = 6x + 6
⇒ 4x = -4
⇒ x = -1
Hence, The required value of x for which XYZA is a rectangle : x = -1