Calculate Rectangle Perimeter: Finding the Distance Around ABCD with Multiple Measurements

Since in a rectangle every pair of opposite sides are equal to each other, we can claim that:

$BC=AD=6$

Therefore:

$$$AD-AE=ED$

Let's substitute the known data into the formula:

$6-3=ED$

$3=ED$

Let's focus on triangle EDF and find side DF using the Pythagorean theorem:

$ED^2+DF^2=EF^2$

Let's substitute the known data into the formula:

$3^2+DF^2=5^2$

$9+DF^2=25$

$DF^2=25-9$

$DF^2=16$

Let's find the square root:

$DF=4$

Side DC=8

Since in a rectangle every pair of opposite sides are equal to each other:

$AD=BC=6$

$AB=CD=8$

Now we can calculate the perimeter of the rectangle by adding all sides together:

$6+8+6+8=12+16=28$