Calculate Rectangle Perimeter: Three Interior Rectangles with 5, 6, and 7 Unit Measurements

Q: Why can't I just add 5 + 6 + 7 to get the perimeter?

These numbers represent measurements within the rectangle, not its outer edges. The perimeter is $ 2(length + width) $ of the outer rectangle ABCD, not the sum of interior segments.

Q: How do I know when there's not enough data?

For a rectangle's perimeter, you need both dimensions. If you can only determine one side length (like AB = 13) but not the other (AD or BC), then there's insufficient data.

Q: What does the diagram tell us exactly?

From the three interior rectangles, we can determine that AB = 7 + 6 = 13. However, we cannot find the length of sides AD or BC from the given information, so we cannot calculate the full perimeter.

Q: Is there a way to find the missing dimensions?

Not with the current information. We would need additional measurements that relate to the height of rectangle ABCD, not just the interior segment lengths shown.

Perimeter Calculations with Insufficient Data

Rectangle ABCD contains three other rectangles.

Calculate the perimeter of 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

00:12 The whole side equals the sum of its parts

00:16 Opposite sides are equal in a rectangle

00:33 We don't have enough data to know the entire sides BC,AD

00:39 Therefore, we cannot determine the rectangle's perimeter

00:43 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.

Calculate the perimeter of ABCD.

Step-by-step solution

Let's look at rectangle EBHF where we are given:

EF=BH=5

FH=EB=6

From this we can calculate AB:

7+6=13

Now we have a pair of sides in rectangle ABCD:

AB=DC=13

We know that EF=BH=AG=5

We therefore do not have enough additional data to calculate the sides AD and BC.

Final Answer

Not enough data

Key Points to Remember

Essential concepts to master this topic

Rectangle Rule: Perimeter requires both length and width dimensions
Analysis Method: From given measurements 5, 6, 7, find AB = 7 + 6 = 13
Data Check: Verify all four sides can be determined from given information ✓

Common Mistakes

Avoid these frequent errors

Adding all visible numbers to find perimeter
Don't just add 5 + 6 + 7 = 18 as the perimeter! These are measurements of interior segments, not the outer rectangle's sides. Always identify which measurements represent the actual perimeter dimensions before calculating.

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 can't I just add 5 + 6 + 7 to get the perimeter?

These numbers represent measurements within the rectangle, not its outer edges. The perimeter is $2(length + width)$ of the outer rectangle ABCD, not the sum of interior segments.

How do I know when there's not enough data?

For a rectangle's perimeter, you need both dimensions. If you can only determine one side length (like AB = 13) but not the other (AD or BC), then there's insufficient data.

What does the diagram tell us exactly?

From the three interior rectangles, we can determine that AB = 7 + 6 = 13. However, we cannot find the length of sides AD or BC from the given information, so we cannot calculate the full perimeter.

Is there a way to find the missing dimensions?

Not with the current information. We would need additional measurements that relate to the height of rectangle ABCD, not just the interior segment lengths shown.

Why is 'Not enough data' sometimes an answer choice?

In real mathematics, problems don't always have solutions with the given information. Recognizing insufficient data is an important mathematical skill - it shows you understand what information is actually needed.

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