Calculate the Perimeter: Rectangle ABCD with Sides 4, 6, and 15 Units

Q: Why can't I just add 4 + 6 + 15 to get the perimeter?

A perimeter requires all four sides of the rectangle! The three numbers given help you find the lengths, but you need to use the fact that opposite sides are equal to determine all four measurements.

Q: How do I know which sides are equal to each other?

In rectangle ABCD, opposite sides are equal: AB = DC and BC = AD. From the diagram, AB = DC = 15, and BC = AD = 6 + 4 = 10.

Q: What does the smaller rectangle inside have to do with this?

The inner rectangle shows that side BC is divided into two parts: 6 units and 4 units. So BC = 6 + 4 = 10 units total.

Q: Why is the answer 50 and not 40?

Because you need two of each side length! Perimeter = 15 + 10 + 15 + 10 = 50. If you only counted each side once (15 + 10 = 25), you'd need to double it.

Q: How can I double-check my perimeter calculation?

Use the formula: $ P = 2(length + width) = 2(15 + 10) = 2(25) = 50 $. This should match adding all four sides individually!

Rectangle Perimeter with Composite Dimensions

What is the perimeter of the given rectangle ABCD?

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's find the perimeter of the rectangle.

00:08 In a rectangle, remember, opposite sides are equal.

00:27 Each side is the sum of its parts.

00:36 So, in a rectangle, opposite sides are equal.

00:44 To find the perimeter, add up all the sides.

00:54 Now, plug the values into the formula to solve for the perimeter.

01:14 And there you have it! This is the solution.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

What is the perimeter of the given rectangle ABCD?

Step-by-step solution

Given that in the smaller rectangle ED=CF=4 (each pair of opposite sides in the rectangle are equal)

We can therefore calculate for the rectangle ABCD that BC=6+4=10

Now we can state in the rectangle ABCD that BC=AD=10

Next we calculate the perimeter of the rectangle by adding together all of the sides:

DC=AB=15

Hence the perimeter of the rectangle ABCD is equal to:

$10+10+15+15=20+30=50$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rectangle Property: Opposite sides are always equal in length
Composite Calculation: BC = 6 + 4 = 10, so AD = 10
Perimeter Check: Add all four sides: 15 + 10 + 15 + 10 = 50 ✓

Common Mistakes

Avoid these frequent errors

Adding only the three given measurements
Don't add 4 + 6 + 15 = 25 and think that's the perimeter! This ignores that rectangles have four sides and opposite sides are equal. Always identify all four side lengths using the rectangle property that opposite sides are equal.

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 4 + 6 + 15 to get the perimeter?

A perimeter requires all four sides of the rectangle! The three numbers given help you find the lengths, but you need to use the fact that opposite sides are equal to determine all four measurements.

How do I know which sides are equal to each other?

In rectangle ABCD, opposite sides are equal: AB = DC and BC = AD. From the diagram, AB = DC = 15, and BC = AD = 6 + 4 = 10.

What does the smaller rectangle inside have to do with this?

The inner rectangle shows that side BC is divided into two parts: 6 units and 4 units. So BC = 6 + 4 = 10 units total.

Why is the answer 50 and not 40?

Because you need two of each side length! Perimeter = 15 + 10 + 15 + 10 = 50. If you only counted each side once (15 + 10 = 25), you'd need to double it.

How can I double-check my perimeter calculation?

Use the formula: $P = 2(length + width) = 2(15 + 10) = 2(25) = 50$ . This should match adding all four sides individually!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Rectangles questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime