Q:

What value of x will make parallelogram ABCD a rhombus? x=

What value of x will make parallelogram ABCD a rhombus? x=

Accepted Solution

A:
The value of x that will make the considered parallelogram ABCD a rhombus is 4 units.What is rhombus and some of its properties?Rhombus is a parallelogram whose all sides are of equal lengths.Its diagonals are perpendicular to each other and they cut each other in half( thus, they're perpendicular bisector of each other).Its vertex angles are bisected by its diagonals.The triangles on either side of the diagonals are isosceles and congruent.For this problem, the missing figure is attached below.We see that the angle between the diagonals is [tex](3x- 12)^\circ[/tex]It is given that ABCD is a parallelogram.For ABCD parallelogram to be a rhombus, its diagonals need to be perpendicular to each other.Perpendicular lines have 90Β° angle between them.Thus, we need:[tex](3x- 12)^\circ = 90^\circ[/tex]Evaluating value of x:[tex](3x- 12)^\circ = 90^\circ\\3x - 12 = 90\\\text{Adding 12 on both the sides}\\3x = 102\\\text{Dividing both the sides by 3}\\\\x = 12/3 = 4[/tex]Thus, the value of x is 4Learn more about rhombus here: