Rectangle Perimeter with Congruent Triangles: Using 5 and 3 Units

Based on the given data, we can claim that:

$OF=OE=3$

$EF=6$

$AB=EF=DC=6$

We'll find side BF using the Pythagorean theorem in triangle BFO:

$OF^2+BF^2=BO^2$

Let's substitute the known values into the formula:

$3^2+BF^2=5^2$

$9+BF^2=25$

$BF^2=25-9$

$BF^2=16$

Let's take the square root:

$BF=4$

Since the triangles overlap:

$BF=DE=4=FC$

From this, we can calculate side BC:

$BC=4+4=8$

Since in a rectangle, each pair of opposite sides are equal to each other, we can claim that AD also equals 8

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

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