Calculate Rectangle Perimeter: Nested Rectangles with Dimensions 6, 4, and 2

Q: Why can't I just use the numbers 6, 4, and 2 that are given?

Those numbers show internal subdivisions of rectangle ABCD, not its complete sides. You need the total length and total width of the outer rectangle to calculate its perimeter.

Q: How do I know if there's enough information?

For rectangle perimeter, you need both the complete length and complete width. If you can't determine either dimension fully from the given information, then there's insufficient data.

Q: What if I can find some of the rectangle's dimensions?

Partial information isn't enough! The perimeter formula $ P = 2(l + w) $ requires complete length and width measurements, not just portions of them.

Q: Could the answer be one of the other numbers like 34 or 42?

No, because we cannot determine the full dimensions of rectangle ABCD from the given information. Any numerical answer would be based on incorrect assumptions about unmeasured segments.

Q: How should I approach similar problems in the future?

Always identify what you need (complete length and width), then check if the given information allows you to find these values. If not, the answer is 'insufficient data'.

Rectangle Perimeter with Insufficient Information

ABCD is a rectangle.

AIFE and EFHG are also rectangles.

Calculate the perimeter of the rectangle ABCD.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the perimeter of rectangle ABCD

00:03 The whole side equals the sum of its parts

00:15 Opposite sides are equal in rectangle ABCD

00:29 Opposite sides are equal in rectangle AEIF

00:40 Opposite sides are equal in rectangle ICGD

00:53 The whole side equals the sum of its parts

01:01 Let's substitute appropriate values and solve for AD

01:08 There isn't enough data, therefore it cannot be determined

01:15 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 is a rectangle.

AIFE and EFHG are also rectangles.

Calculate the perimeter of the rectangle ABCD.

Step-by-step solution

To solve this problem, we'll need to determine if all required dimensions for calculating the perimeter of rectangle $ABCD$ are present:

We'll start by defining the perimeter formula for the rectangle, $P = 2(l + w)$ .
Identify any given lengths in the diagram available for $ABCD$ : It's given that $AB = 6$ and presumably $BC = 2$ .
Interpret the given rectangle data in context with the diagram, checking if the other length and width of $ABCD$ can be determined from $AIFE$ and $EFHG$ .

After reviewing the data and the diagram details, it becomes apparent that specific side lengths for segments $AD$ or any missing lengths on line $AB$ would not be directly deducible from the description provided.

Therefore, due to insufficient information provided to ascertain the entire length or width of rectangle $ABCD$ and thereby its complete perimeter, we conclude that:

The correct answer to the problem is: Not enough data.

Final Answer

Not enough data

Key Points to Remember

Essential concepts to master this topic

Perimeter Formula: For rectangles, $P = 2(length + width)$
Information Analysis: Check if all required dimensions are given or determinable
Verification: Count available measurements against formula requirements ✓

Common Mistakes

Avoid these frequent errors

Assuming all visible dimensions can determine the full perimeter
Don't add up partial measurements like 6 + 4 + 2 + 2 = 14 and double it! This uses internal subdivisions, not the actual rectangle sides. Always identify the complete length and width of the target rectangle ABCD before applying the perimeter formula.

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle below.

Side DC has a length of 1.5 cm and side AD has a length of 9.5 cm.

What is the perimeter of the rectangle?

FAQ

Everything you need to know about this question

Why can't I just use the numbers 6, 4, and 2 that are given?

Those numbers show internal subdivisions of rectangle ABCD, not its complete sides. You need the total length and total width of the outer rectangle to calculate its perimeter.

How do I know if there's enough information?

For rectangle perimeter, you need both the complete length and complete width. If you can't determine either dimension fully from the given information, then there's insufficient data.

What if I can find some of the rectangle's dimensions?

Partial information isn't enough! The perimeter formula $P = 2(l + w)$ requires complete length and width measurements, not just portions of them.

Could the answer be one of the other numbers like 34 or 42?

No, because we cannot determine the full dimensions of rectangle ABCD from the given information. Any numerical answer would be based on incorrect assumptions about unmeasured segments.

How should I approach similar problems in the future?

Always identify what you need (complete length and width), then check if the given information allows you to find these values. If not, the answer is 'insufficient data'.

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