Calculate Rectangle Perimeter: Finding the Distance Around ABCD with Given Dimensions 7, 5, and 1

Rectangle Perimeter with Insufficient Information

AAABBBCCCDDDEEEFFF751Determine 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 the rectangle ABCD
00:03 Opposite sides are equal in a rectangle
00:12 The whole side equals the sum of its parts
00:17 Substitute in the relevant values and solve for AB
00:23 We don't have enough data to determine the perimeter
00:26 This is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

AAABBBCCCDDDEEEFFF751Determine the perimeter of the rectangle ABCD:

2

Step-by-step solution

Based on the given data, we know that:

AD=BC=5 AD=BC=5

AB=AE+EB AB=AE+EB

AB=7+EB AB=7+EB

We are missing data to determine the length of AB, and therefore we cannot calculate the perimeter of the rectangle

3

Final Answer

It is not possible to know

Key Points to Remember

Essential concepts to master this topic
  • Rectangle Formula: Perimeter = 2(length + width) requires both dimensions
  • Analysis: Given AD = 5, AE = 7, but AB length is unknown
  • Check: Verify all four sides are known before calculating perimeter ✓

Common Mistakes

Avoid these frequent errors
  • Assuming AB equals AE
    Don't think AB = 7 just because AE = 7! Point E is on side AB, so AB = AE + EB = 7 + EB, where EB is unknown. Always identify what each measurement represents before calculating.

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?

1.51.51.5AAABBBCCCDDD9.5

FAQ

Everything you need to know about this question

Why can't I just use the given numbers 7, 5, and 1?

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These numbers represent different segments, not the rectangle's sides! We have AD = 5 (one side), AE = 7 (part of AB), and FC = 1 (another partial segment). We need the complete lengths of all four sides.

What does it mean that E is on side AB?

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Point E divides side AB into two parts: AE and EB. So AB = AE + EB = 7 + EB. Since we don't know EB's length, we can't find AB's total length.

How do I know when I have enough information?

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For a rectangle's perimeter, you need both the length and width. If any measurement is incomplete or represents only part of a side, you cannot calculate the perimeter.

Could the answer be 25 or 38?

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No! These would require assuming unknown lengths. For example, 25 assumes AB = 10, but we have no evidence for this. Never guess missing information in geometry problems.

What should I do when information is missing?

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Always choose 'It is not possible to know' when you cannot determine all required measurements. This shows you understand what information is actually needed for the calculation.

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