Parallelogram Perimeter Problem: Solving for X when Perimeter is 80 cm

The parallelogram ABCD has a perimeter equal to 80 cm.

Calculate X.

XXX2X2X2XAAABBBCCCDDD

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:06 Let's find the value of X.
00:10 Remember, the perimeter of a parallelogram is the sum of all its sides.
00:15 In a parallelogram, opposite sides are equal. So, multiply each pair of sides.
00:21 Now, plug in the values you have, and solve for X.
00:26 Next, combine like terms together.
00:30 Then, isolate X to find its value.
00:37 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

The parallelogram ABCD has a perimeter equal to 80 cm.

Calculate X.

XXX2X2X2XAAABBBCCCDDD

2

Step-by-step solution

Since in a parallelogram each pair of opposite sides are equal and parallel:

BC=AD=2x BC=AD=2x

AB=CD=x AB=CD=x

Now let's substitute the known data into the formula for calculating the perimeter:

80=2x×2+2×x 80=2x\times2+2\times x

80=4x+2x 80=4x+2x

80=6x 80=6x

Let's divide both terms by 6:

806=6x6 \frac{80}{6}=\frac{6x}{6}

806=x \frac{80}{6}=x

Let's simplify the fraction by 2

403=x \frac{40}{3}=x

3

Final Answer

x=403 x=\frac{40}{3}

Practice Quiz

Test your knowledge with interactive questions

Given the parallelogram:

444222AAABBBDDDCCC

Calculate the perimeter of the parallelogram.

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