Answer: Third option.
Step-by-step explanation:
The missing figure is attached.
The perimeter of a rectangle can be calculated with:
[tex]P=2l+2w[/tex]
Where "l" is the length and "w" is the width.
We can see that the width of this rectangle is:
[tex]w=12\ units[/tex]
So, we need to find the lenght.
Let be P the point of intersection of the diagonals.
The diagonals of a rectangle are equal.
Since:
[tex]JM=12\\MO=10[/tex]
We know that, by definition:
[tex]JP=LP=MP=KP[/tex]
Then, we can find the lenght of the rectangle by using the Pythagorean Theorem:
[tex]MK^2=KL^2+LM^2[/tex]
We can identify that:
[tex]MK=10\ units+10\ units=20\ units\\KL=12\ units[/tex]
Then, subsituting values and solving for "LM", we get:
[tex]20^2=LM^2+12^2\\\\LM=\sqrt{20^2-12^2}\\\\LM=16\ units[/tex]
Substituting values into the formula for calculate the perimeter, we get:
[tex]P=2(16}\ units)+2(12\ units)=56\ units[/tex]
