Calculate Rectangle Perimeter: Finding the Distance Around ABCD with Multiple Measurements

Q: Why can't I just add all the given numbers (3 + 6 + 5 + 4)?

Those numbers represent different types of measurements! The 5 is a diagonal inside the rectangle, not a side. Only use the actual rectangle side lengths for perimeter calculations.

Q: How do I know which sides are equal in a rectangle?

In rectangle ABCD, opposite sides are always equal: AB = CD (top and bottom) and AD = BC (left and right sides). Use this property to find unknown side lengths.

Q: What if I get confused about which measurement goes where?

Draw the rectangle yourself and label each measurement carefully. Look for right angles and use the given information to identify what each number represents before calculating.

Q: How can I check if my perimeter is correct?

Verify that your rectangle sides make sense: opposite sides should be equal and the measurements should fit with any given diagonal or internal segments using geometry rules.

Rectangle Perimeter with Pythagorean Application

Look at the rectangle below:

Calculate the perimeter of rectangle ABCD.

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the perimeter of the rectangle

00:03 Opposite sides are equal in a rectangle

00:14 ED equals the side (AD) minus AE

00:25 Substitute in the relevant values according to the given data and proceed to solve for ED

00:38 This is the value of the side ED

00:43 Apply the Pythagorean theorem to the triangle EDF to determine DF

00:54 Substitute in the relevant values according to the given data and solve for DF

01:10 Isolate DF

01:28 This is the value of DF

01:32 The entire side (DC) equals the sum of its parts (DF+FC)

01:44 Substitute the relevant values into the formula and solve for the side DC

01:48 This is the length of the side DC

01:54 Opposite sides are equal in a rectangle

01:57 The perimeter of the rectangle equals the sum of its sides

02:04 Substitute in the relevant values and solve for the perimeter

02:21 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the rectangle below:

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:

$BC=AD=6$

Therefore:

$AD-AE=ED$

Let's substitute the known data into the formula:

$6-3=ED$

$3=ED$

Let's focus on triangle EDF and find side DF using the Pythagorean theorem:

$ED^2+DF^2=EF^2$

Let's substitute the known data into the formula:

$3^2+DF^2=5^2$

$9+DF^2=25$

$DF^2=25-9$

$DF^2=16$

Let's find the square root:

$DF=4$

Side DC=8

Since in a rectangle every pair of opposite sides are equal to each other:

$AD=BC=6$

$AB=CD=8$

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

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

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rectangle Property: Opposite sides are equal, so AD = BC and AB = CD
Pythagorean Theorem: In right triangle EDF, $3^2 + 4^2 = 5^2$ gives DF = 4
Perimeter Check: Add all four sides: 6 + 8 + 6 + 8 = 28 ✓

Common Mistakes

Avoid these frequent errors

Using given measurements as direct side lengths
Don't assume the diagonal measurement EF = 5 is a side length = wrong perimeter calculation! The diagonal connects interior points, not rectangle corners. Always identify which measurements represent actual rectangle sides versus internal segments.

Practice Quiz

Test your knowledge with interactive questions

Calculate the perimeter of the rectangle below.

FAQ

Everything you need to know about this question

Why can't I just add all the given numbers (3 + 6 + 5 + 4)?

Those numbers represent different types of measurements! The 5 is a diagonal inside the rectangle, not a side. Only use the actual rectangle side lengths for perimeter calculations.

How do I know which sides are equal in a rectangle?

In rectangle ABCD, opposite sides are always equal: AB = CD (top and bottom) and AD = BC (left and right sides). Use this property to find unknown side lengths.

Why do I need to use the Pythagorean theorem here?

The Pythagorean theorem helps find the missing length DF in the right triangle. Since EF = 5 is the hypotenuse and ED = 3, we can calculate DF = 4, which gives us the full rectangle width.

What if I get confused about which measurement goes where?

Draw the rectangle yourself and label each measurement carefully. Look for right angles and use the given information to identify what each number represents before calculating.

How can I check if my perimeter is correct?

Verify that your rectangle sides make sense: opposite sides should be equal and the measurements should fit with any given diagonal or internal segments using geometry rules.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Rectangles questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime