Rectangle Perimeter: Calculate ABCD with Equal Segments CE and AB

Video Solution

Solution Steps

00:06 Let's calculate the perimeter of rectangle, A. B. C. D.

00:10 Remember! Opposite sides are equal in a rectangle.

00:17 For segment F. C., it's the entire side B. C. minus segment B. F.

00:23 Now, plug in the given values to find F. C. and solve it step by step.

00:37 Great job! That's the height, F. C.

00:41 Next, use the Pythagorean theorem on triangle F. C. E. to find C. E.

00:51 Again, insert the values into the formula, and solve for C. E.

01:08 Let's isolate C. E. You're doing great!

01:27 Nice work! That's the length of side C. E.

01:32 According to the data, sides are equal. Keep this in mind.

01:41 And remember, opposite sides are always equal in a rectangle.

01:54 The perimeter is simply the sum of all sides.

01:58 Plug in the values and solve for the perimeter. Almost there!

02:21 Awesome! That's the solution. Well done!

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:

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