Calculate Rectangle ABCD Perimeter: Nested Rectangles with Measurements 3, 5, 6, and 7

Q: How do I know which measurements to add together?

Look at the diagram carefully! Add measurements that are in the same direction. For width: 7 + 6 = 13. For height: 5 + 3 = 8.

Q: Why can't I just add all the numbers I see?

The numbers 3, 5, 6, and 7 are internal measurements of smaller rectangles, not the sides of rectangle ABCD. You need to combine them to find the actual dimensions.

Q: How do I identify the length and width of the big rectangle?

Trace along each side of rectangle ABCD. The horizontal sides go from A to B and D to C (length = 7 + 6 = 13). The vertical sides go from A to D and B to C (width = 5 + 3 = 8).

Q: What if the internal rectangles were arranged differently?

The principle stays the same! Always add up measurements along each complete side of the outer rectangle, regardless of how the internal rectangles are positioned.

Q: Do I need to find the area of the internal rectangles?

No! This question only asks for the perimeter of the outer rectangle ABCD. Focus on finding its length and width, then use $ P = 2(l + w) $.

Rectangle Perimeter with Internal Subdivisions

Rectangle ABCD contains three other rectangles inside of it.

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 rectangle ABCD

00:08 Opposite sides are equal in rectangle EBHF

00:50 The whole side equals the sum of its parts

00:57 Opposite sides are equal in rectangle ABCD

01:08 The whole side equals the sum of its parts

01:19 Opposite sides are equal in rectangle ABCD

01:22 The perimeter of the rectangle equals the sum of its sides

01:32 Let's substitute appropriate values and solve for the perimeter

01:55 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Rectangle ABCD contains three other rectangles inside of it.

Calculate the perimeter of rectangle ABCD.

Step-by-step solution

Since in a rectangle, each pair of opposite sides are equal to one another, we can deduce that:

$EF=BH=AG=5$

We can calculate side AD:

$5+3=8$

Since side AD is equal to side BC, it is also equal to 8

$FH=EB=6$

Now we can calculate side AB:

$7+6=13$

Since side AB is equal to side CD, it is also equal to 13

Let's calculate the perimeter of rectangle ABCD:

$8+13+8+13=16+26=42$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rectangle Property: Opposite sides are equal in length
Technique: Add measurements along each direction: 7 + 6 = 13
Check: Verify perimeter: 13 + 8 + 13 + 8 = 42 ✓

Common Mistakes

Avoid these frequent errors

Adding all given measurements directly
Don't add 3 + 5 + 6 + 7 = 21 as the perimeter! These are internal measurements, not the rectangle's sides. Always determine the full length and width by adding measurements in each direction first.

Practice Quiz

Test your knowledge with interactive questions

Calculate the perimeter of the rectangle below.

FAQ

Everything you need to know about this question

How do I know which measurements to add together?

Look at the diagram carefully! Add measurements that are in the same direction. For width: 7 + 6 = 13. For height: 5 + 3 = 8.

Why can't I just add all the numbers I see?

The numbers 3, 5, 6, and 7 are internal measurements of smaller rectangles, not the sides of rectangle ABCD. You need to combine them to find the actual dimensions.

How do I identify the length and width of the big rectangle?

Trace along each side of rectangle ABCD. The horizontal sides go from A to B and D to C (length = 7 + 6 = 13). The vertical sides go from A to D and B to C (width = 5 + 3 = 8).

What if the internal rectangles were arranged differently?

The principle stays the same! Always add up measurements along each complete side of the outer rectangle, regardless of how the internal rectangles are positioned.

Do I need to find the area of the internal rectangles?

No! This question only asks for the perimeter of the outer rectangle ABCD. Focus on finding its length and width, then use $P = 2(l + w)$ .

🌟 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