Parallelogram Perimeter: Express Total Length When One Side is 2X

A parallelogram has one side that is 2 times longer than the other. The length of the smaller side is X.

AAABBBDDDCCC

Express the circumference of the parallelogram in terms of X.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Express the perimeter of the parallelogram using X
00:03 Opposite sides are equal in a parallelogram
00:10 The larger pair of sides
00:16 The side length according to the given data
00:22 The ratio of sides according to the given data
00:29 Substitute the side value to find AB
00:34 Opposite sides are equal in a parallelogram
00:43 The perimeter of the parallelogram equals the sum of its sides
00:55 Substitute appropriate values and solve to find the perimeter
01:06 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

A parallelogram has one side that is 2 times longer than the other. The length of the smaller side is X.

AAABBBDDDCCC

Express the circumference of the parallelogram in terms of X.

2

Step-by-step solution

As is true of a parallelogram each pair of opposite sides are equal to one another

AB=CD,AC=BD AB=CD,AC=BD

Given that AB>AC AB > AC

Let's call AC by the name X and therefore:

AB=2AC=2×x=2x AB=2AC=2\times x=2x

Now we know that:

AB=CD=2x,AC=BD=x AB=CD=2x,AC=BD=x

The perimeter is equal to the sum of all the sides together:

2x+x+2x+x=6x 2x+x+2x+x=6x

3

Final Answer

4X+4

Practice Quiz

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Given the parallelogram:

444222AAABBBDDDCCC

Calculate the perimeter of the parallelogram.

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