Rectangle Perimeter: Calculate ABCD with Equal Segments CE and AB

Q: Why do I need to find FC before using the Pythagorean theorem?

You need two sides of the right triangle to find the third! Since you know BC=11 and BF=3, you can calculate FC = 11-3 = 8. Now you have FC=8 and FE=17 to find CE.

Q: What does CE = AB actually mean?

This is a given condition that helps verify your answer! After calculating CE using the Pythagorean theorem, you can use this fact to determine that AB = CE = 15.

Q: What if I calculated CE wrong?

Double-check your Pythagorean calculation: $ 8^2 + CE^2 = 17^2 $ means $ CE^2 = 289 - 64 = 225 $, so $ CE = \sqrt{225} = 15 $.

Pythagorean Theorem with Rectangle Extensions

Look at the following rectangle:

CE = AB

Calculate the perimeter of rectangle ABCD.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

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 written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the following rectangle:

CE = AB

Calculate the perimeter of rectangle ABCD.

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:

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

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rectangle Properties: Opposite sides are equal, use given measurements wisely
Pythagorean Technique: $8^2 + CE^2 = 17^2$ gives CE = 15
Check: Perimeter 11+15+11+15 = 52, verify CE=AB condition ✓

Common Mistakes

Avoid these frequent errors

Forgetting to use rectangle properties
Don't assume you need to find all side lengths separately = wasted work and confusion! Students often miss that opposite sides are equal in rectangles. Always use rectangle properties: if AD=11, then BC=11 automatically.

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle ABCD below.

Side AB is 6 cm long and side BC is 4 cm long.

What is the area of the rectangle?

FAQ

Everything you need to know about this question

Why do I need to find FC before using the Pythagorean theorem?

You need two sides of the right triangle to find the third! Since you know BC=11 and BF=3, you can calculate FC = 11-3 = 8. Now you have FC=8 and FE=17 to find CE.

How do I know triangle FCE is a right triangle?

Look at the diagram carefully! Point F is on side BC, creating a right angle at F. The rectangle's sides are perpendicular, so CF is perpendicular to CE.

What does CE = AB actually mean?

This is a given condition that helps verify your answer! After calculating CE using the Pythagorean theorem, you can use this fact to determine that AB = CE = 15.

Can I solve this without the Pythagorean theorem?

No, because point E extends beyond the rectangle! The only way to find CE is through the right triangle FCE. The Pythagorean theorem is essential for this type of problem.

Why is the perimeter 52 and not just 44?

Don't confuse the rectangle ABCD with the extended figure! The rectangle has sides AB=CD=15 and AD=BC=11, so perimeter = 2(15+11) = 52.

What if I calculated CE wrong?

Double-check your Pythagorean calculation: $8^2 + CE^2 = 17^2$ means $CE^2 = 289 - 64 = 225$ , so $CE = \sqrt{225} = 15$ .

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