Calculate Rectangle Perimeter: 10 x 6 ABCD Rectangle

Look at the following rectangle:

AAABBBCCCDDD106

Calculate the perimeter of the 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
00:00 Calculate the perimeter of the rectangle
00:03 Apply the Pythagorean theorem to the triangle BCD
00:15 Substitute in the relevant values according to the given data and proceed to solve for DC
00:33 Isolate DC
00:48 This is the length of the side DC
00:57 Opposite sides are equal in a rectangle
01:12 The perimeter of the rectangle equals the sum of its sides
01:20 Substitute in the relevant values and solve for the perimeter
01:45 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Look at the following rectangle:

AAABBBCCCDDD106

Calculate the perimeter of the rectangle ABCD.

2

Step-by-step solution

Let's focus on triangle BCD in order to find side DC.

We'll use the Pythagorean theorem and input the known data:

BC2+DC2=BD2 BC^2+DC^2=BD^2

62+DC2=102 6^2+DC^2=10^2

DC2=10036=64 DC^2=100-36=64

Let's now remove the square root:

DC=8 DC=8

Since in a rectangle each pair of opposite sides are equal to each other, we know that:

DC=AB=8 DC=AB=8

BC=AD=6 BC=AD=6

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

8+6+8+6=16+12=28 8+6+8+6=16+12=28

3

Final Answer

28

Practice Quiz

Test your knowledge with interactive questions

The points A and O are shown in the figure below.

Is it possible to draw a rectangle so that the side AO is its diagonal?

AAAOOO

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Pythagorean Theorem 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

More Questions

Click on any question to see the complete solution with step-by-step explanations