Note: Consider J is the intersection point of diagonals of quadrilateral FGHI.
Given:
[tex]GJ=11a[/tex]
[tex]IJ=a+10[/tex]
To find:
The value of a that makes quadrilateral FGHI a parallelogram.
Solution:
We know that the diagonals of a parallelogram bisect each other.
If FGHI is a parallelogram and J is the intersection point of diagonals, then
[tex]GJ=IJ[/tex]
[tex]11a=a+10[/tex]
[tex]11a-a=10[/tex]
[tex]10a=10[/tex]
Divide both sides by 10.
[tex]a=\dfrac{10}{10}[/tex]
[tex]a=1[/tex]
Therefore, the required value of a is 1 units.
