Calculate Rectangle Perimeter: Finding the Border Length of EFCD (3×5)

Q: How do I know which rectangle to measure?

The problem asks for rectangle EFCD, not the whole figure. Look for the four vertices E, F, C, D and trace their outline to identify the correct rectangle.

Q: Why is ED equal to 2 if it's not labeled?

Since AE = 3 and the whole side AD = 5, we can find ED by subtraction: $ ED = AD - AE = 5 - 3 = 2 $.

Q: How do I know that FC also equals 2?

In a rectangle, opposite sides are equal. Since ED = 2, then FC (the opposite side) must also equal 2.

Q: What if I get confused about which sides belong to rectangle EFCD?

List the four sides in order: EF, FC, CD, DE. From the diagram: EF = 7, FC = 2, CD = 7, DE = 2. Then add: $ 7 + 2 + 7 + 2 = 18 $.

Q: Can I use the perimeter formula P = 2(length + width)?

Yes! Rectangle EFCD has length = 7 and width = 2, so $ P = 2(7 + 2) = 2(9) = 18 $. This matches adding all four sides individually.

Rectangle Perimeter with Partial Side Measurements

Look at the following rectangle:

What is the perimeter of the rectangle EFCD?

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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 EFCD

00:03 Opposite sides are equal in a rectangle

00:11 The segment (ED) equals the entire side (AD) minus the segment (AE)

00:16 Substitute in the relevant values to the formula and proceed to solve for ED

00:31 This is the value of the side ED, opposite sides in a rectangle are equal

00:42 Opposite sides in a rectangle are equal

00:55 The perimeter of the rectangle equals the sum of its sides

01:04 Substitute in the relevant values and proceed to solve for the perimeter

01:28 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the following rectangle:

What is the perimeter of the rectangle EFCD?

Step-by-step solution

Since every pair of opposite sides are equal in a rectangle, we know that:

$BC=AD=5$

Now we can calculate side ED:

$AD-AE=ED$

Let's substitute in the known data:

$5-3=ED$

$ED=2$

Side ED is equal to side FC and therefore also equal to 2.

We also know that:

$AB=CD=EF=7$

Now we can calculate the perimeter of rectangle EFCD:

$2+7+2+7=4+14=18$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rectangle Property: Opposite sides are always equal in length
Technique: Use subtraction to find missing segments: 5 - 3 = 2
Check: Add all four sides of EFCD: 2 + 7 + 2 + 7 = 18 ✓

Common Mistakes

Avoid these frequent errors

Using the wrong rectangle's measurements
Don't calculate the perimeter of the entire rectangle ABCD = 2(7) + 2(5) = 24! This ignores that EFCD is a smaller rectangle inside. Always identify which specific rectangle you need and use only its four sides.

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

How do I know which rectangle to measure?

The problem asks for rectangle EFCD, not the whole figure. Look for the four vertices E, F, C, D and trace their outline to identify the correct rectangle.

Why is ED equal to 2 if it's not labeled?

Since AE = 3 and the whole side AD = 5, we can find ED by subtraction: $ED = AD - AE = 5 - 3 = 2$ .

How do I know that FC also equals 2?

In a rectangle, opposite sides are equal. Since ED = 2, then FC (the opposite side) must also equal 2.

What if I get confused about which sides belong to rectangle EFCD?

List the four sides in order: EF, FC, CD, DE. From the diagram: EF = 7, FC = 2, CD = 7, DE = 2. Then add: $7 + 2 + 7 + 2 = 18$ .

Can I use the perimeter formula P = 2(length + width)?

Yes! Rectangle EFCD has length = 7 and width = 2, so $P = 2(7 + 2) = 2(9) = 18$ . This matches adding all four sides individually.

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