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
00:11 Let's express the perimeter of the parallelogram using the variable X.
00:16 Remember: In a parallelogram, opposite sides are always equal.
00:22 Let's look at the longer sides first.
00:27 Based on the data, here's the length of one side.
00:33 Next, examine the given ratio of the sides.
00:40 Substitute this side value to calculate A B.
00:45 Remember: Opposite sides are equal in a parallelogram.
00:54 The perimeter is simply the total sum of all sides.
01:06 Now, plug in the correct values and solve to find the perimeter.
01:17 And that's how you find the solution to this problem!

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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