Rectangle Perimeter Problem: Calculate ABCD with Given Dimensions 9, 5, and 3

Q: How do I know which dimensions belong to which rectangle?

Look carefully at the labels on the diagram. The number 9 is on side AB, 5 is on side AE, and 3 is on side FC. Use these to identify which sides belong to each rectangle.

Q: What if I can't see all the rectangles clearly?

Focus on the three rectangle names given: ABCD, EFCD, and ABFE. Each name tells you the four corners of that rectangle. Use the overlapping sides to figure out the relationships.

Q: Can I solve this without finding all four sides?

No! The perimeter of a rectangle requires all four sides. Even though opposite sides are equal, you still need to identify the length and width before using the perimeter formula.

Q: What's the easiest way to check my perimeter answer?

Use the formula $ P = 2(l + w) $. With length = 9 and width = 8, you get $ P = 2(9 + 8) = 2(17) = 34 $. This should match adding all four sides: 9 + 8 + 9 + 8 = 34 ✓

Rectangle Perimeter with Composite Shapes

ABCD, EFCD, and ABFE are all rectangles.

Calculate the perimeter of rectangle ABCD.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the perimeter of rectangle ABCD

00:03 Opposite sides are equal in a rectangle

00:10 The whole side equals the sum of its parts

00:24 Opposite sides are equal in a rectangle

00:31 The perimeter of the rectangle equals the sum of its sides

00:47 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

ABCD, EFCD, and ABFE are all rectangles.

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:

$AE=BF=5$

$AB=CD=9$

Now we can calculate side BC:

$5+3=8$

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

Let's calculate the perimeter of rectangle ABCD:

$9+8+9+8=18+16=34$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rectangle Property: Opposite sides are equal in length
Technique: Add dimensions to find missing sides: 5 + 3 = 8
Check: Perimeter formula 2(length + width) = 2(9 + 8) = 34 ✓

Common Mistakes

Avoid these frequent errors

Using only the given dimensions without finding all sides
Don't just add 9 + 5 + 3 = 17 as the perimeter! This ignores that rectangles have four sides and you need to find the missing dimensions first. Always identify all four sides before calculating perimeter.

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

How do I know which dimensions belong to which rectangle?

Look carefully at the labels on the diagram. The number 9 is on side AB, 5 is on side AE, and 3 is on side FC. Use these to identify which sides belong to each rectangle.

Why do I need to add 5 + 3 to get side BC?

Because rectangle ABCD is divided into two smaller rectangles. Side BC is made up of side BE (which equals 5) plus side EC (which equals 3), so BC = 5 + 3 = 8.

What if I can't see all the rectangles clearly?

Focus on the three rectangle names given: ABCD, EFCD, and ABFE. Each name tells you the four corners of that rectangle. Use the overlapping sides to figure out the relationships.

How do I know that AE = BF = 5?

In rectangle ABFE, opposite sides are equal. Since AE = 5 (given), then BF must also equal 5. This is a fundamental property of rectangles.

Can I solve this without finding all four sides?

No! The perimeter of a rectangle requires all four sides. Even though opposite sides are equal, you still need to identify the length and width before using the perimeter formula.

What's the easiest way to check my perimeter answer?

Use the formula $P = 2(l + w)$ . With length = 9 and width = 8, you get $P = 2(9 + 8) = 2(17) = 34$ . This should match adding all four sides: 9 + 8 + 9 + 8 = 34 ✓

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