Solve for X: Perimeter of 44 in a Compound Rectangle with 10x-8 Side Length

Q: Why do I need to add all four sides instead of using 2(length + width)?

The formula 2(length + width) only works for simple rectangles. This compound rectangle has an L-shape where the outer perimeter includes edges of different lengths. Always trace around the outside edge!

Q: How do I identify which sides to include in the perimeter?

Look for rectangle GDEF and trace around its outer boundary. The perimeter includes: GF (bottom), FE (right), ED (top), and DG (left side going up and across).

Q: What if I get confused about which expression goes where?

Use the diagram labels! The expressions 10x-8, 5x, and 3+x are positioned next to their corresponding sides. Match each label to its side carefully.

Q: Why does my algebra give 30x - 16 = 44?

You have two sides of length $ 10x-8 $ and two sides of length $ 5x $. So: $ 2(10x-8) + 2(5x) = 20x-16+10x = 30x-16 $.

Q: How can I check if x = 2 is really correct?

Substitute back: $ 10(2)-8 = 12 $ and $ 5(2) = 10 $. So perimeter = $ 12+12+10+10 = 44 $ ✓

Rectangle Perimeter with Algebraic Expressions

The rectangle in the diagram is composed of of three smaller rectangles.

Calculate x given that GDEF has a perimeter of 44.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 In a rectangle with equal opposite sides

00:07 Substitute the side value according to the given data

00:14 In a rectangle with equal opposite sides

00:17 Substitute the side value according to the given data

00:24 The perimeter of the rectangle equals the sum of its sides

00:33 Substitute appropriate values according to the given data and solve for X

00:54 Group terms

01:06 Isolate X

01:22 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The rectangle in the diagram is composed of of three smaller rectangles.

Calculate x given that GDEF has a perimeter of 44.

Step-by-step solution

Let's calculate the perimeter of rectangle GDEF using the given data:

$10x-8+10x-8+5x+5x=44$

We'll group similar terms:

$30x-16=44$

$30x=44+16$

$30x=60$

$x=2$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Perimeter Rule: Add all four sides of rectangle together
Technique: Combine like terms: $10x-8+10x-8+5x+5x = 30x-16$
Check: Substitute x=2: $30(2)-16 = 60-16 = 44$ ✓

Common Mistakes

Avoid these frequent errors

Adding only opposite sides instead of all four sides
Don't just add length + width and multiply by 2 = wrong perimeter! Compound rectangles have irregular shapes where opposite sides aren't always equal. Always identify and add all four outer edges of the complete shape.

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 do I need to add all four sides instead of using 2(length + width)?

The formula 2(length + width) only works for simple rectangles. This compound rectangle has an L-shape where the outer perimeter includes edges of different lengths. Always trace around the outside edge!

How do I identify which sides to include in the perimeter?

Look for rectangle GDEF and trace around its outer boundary. The perimeter includes: GF (bottom), FE (right), ED (top), and DG (left side going up and across).

What if I get confused about which expression goes where?

Use the diagram labels! The expressions 10x-8, 5x, and 3+x are positioned next to their corresponding sides. Match each label to its side carefully.

Why does my algebra give 30x - 16 = 44?

You have two sides of length $10x-8$ and two sides of length $5x$ . So: $2(10x-8) + 2(5x) = 20x-16+10x = 30x-16$ .

How can I check if x = 2 is really correct?

Substitute back: $10(2)-8 = 12$ and $5(2) = 10$ . So perimeter = $12+12+10+10 = 44$ ✓

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