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

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

Calculate x given that GDEF has a perimeter of 44.

AAABBBCCCGGGFFFDDDEEE10x-83+x5x

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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

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1

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.

AAABBBCCCGGGFFFDDDEEE10x-83+x5x

2

Step-by-step solution

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

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

We'll group similar terms:

30x−16=44 30x-16=44

30x=44+16 30x=44+16

30x=60 30x=60

x=2 x=2

3

Final Answer

2

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?

1.51.51.5AAABBBCCCDDD9.5

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