Rectangle Perimeter: Calculate ABCD with Equal Segments CE and AB

Look at the following rectangle:

CE = AB

Calculate the perimeter of rectangle ABCD.

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

$AD=BC=11$

We can calculate side FC:

$11-3=FC$

$8=FC$

Let's focus on triangle FCE and calculate side CE using the Pythagorean theorem:

$CF^2+CE^2=FE^2$

Let's substitute the known values into the formula:

$8^2+CE^2=17^2$

$64+CE^2=289$

$CE^2=289-64$

$CE^2=225$

Let's take the square root:

$CE=15$

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

$CE=AB=CD=15$

Now we can calculate the perimeter of the rectangle:

$11+15+11+15=22+30=52$