Calculate Rectangle Perimeter: 10 x 6 ABCD Rectangle

Rectangle Perimeter with Pythagorean Theorem

Look at the following rectangle:

AAABBBCCCDDD106

Calculate the perimeter of the rectangle ABCD.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:05 Let's find the perimeter of this rectangle.
00:08 First, use the Pythagorean theorem on triangle BCD.
00:20 Plug in the values you have to solve for side D C.
00:38 Now, focus on getting D C by itself.
00:53 You've found the length for side D C.
01:02 Remember, opposite sides in a rectangle are equal.
01:17 The perimeter adds up all these side lengths.
01:25 Substitute the values and calculate the perimeter.
01:50 Great job! That's how you find the perimeter.

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

Key Points to Remember

Essential concepts to master this topic
  • Rectangle Property: Opposite sides are equal, all angles are 90°
  • Pythagorean Theorem: Use a2+b2=c2 a^2 + b^2 = c^2 to find unknown side
  • Check: Verify 62+82=102 6^2 + 8^2 = 10^2 gives 36 + 64 = 100 ✓

Common Mistakes

Avoid these frequent errors
  • Assuming the diagonal is a side of the rectangle
    Don't add the diagonal (10) when calculating perimeter = gives 32 instead of 28! The diagonal connects opposite corners, not a side. Always identify the four actual sides: two lengths and two widths.

Practice Quiz

Test your knowledge with interactive questions

Calculate the perimeter of the rectangle below.

181818222

FAQ

Everything you need to know about this question

Why can't I just add 10 + 6 + 10 + 6?

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The diagonal (10) is not a side of the rectangle! It cuts through the middle. You need to find the actual side length using the Pythagorean theorem first.

How do I know which sides are equal in a rectangle?

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In rectangle ABCD, opposite sides are always equal: AB = DC and AD = BC. Think of it like a door frame - the top equals the bottom, left equals right.

What if I get a decimal when using the Pythagorean theorem?

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Sometimes you'll get decimals or square roots that don't simplify nicely. In this problem, 64=8 \sqrt{64} = 8 works out perfectly, but always double-check your arithmetic!

Can I use the Pythagorean theorem on any rectangle?

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Yes! Every rectangle forms right triangles when you draw a diagonal. The diagonal is always the hypotenuse, and the two sides are the legs of the right triangle.

What's the difference between area and perimeter?

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Perimeter is the distance around the rectangle (add all sides). Area is the space inside the rectangle (multiply length × width). This problem asks for perimeter!

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