Rectangle Perimeter: Calculate ABCD with Equal Segments CE and AB

Video Solution

Solution Steps

00:00 Calculate the perimeter of rectangle ABCD

00:03 Opposite sides are equal in a rectangle

00:11 Segment FC equals the entire side (BC) minus segment (BF)

00:16 Let's substitute appropriate values according to the given data and solve for FC

00:31 This is the height FC

00:35 We'll use the Pythagorean theorem in triangle FCE to find CE

00:45 Let's substitute appropriate values and solve for CE

01:02 Let's isolate CE

01:21 This is the length of side CE

01:26 Sides are equal according to the given data

01:35 Opposite sides are equal in a rectangle

01:48 The perimeter of the rectangle equals the sum of its sides

01:52 Let's substitute appropriate values and solve for the perimeter

02:15 And this is the solution to the problem

Step-by-Step Solution

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:

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