Calculate Side Length AD in a Parallelogram with Perimeter 24cm and AB = 8

A parallelogram has a perimeter of 24 cm.

AB = 8

How long is side AD?

888DDDAAABBBCCC

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find AD
00:03 The perimeter of the parallelogram equals the sum of the sides
00:06 Opposite sides are equal in a parallelogram, so multiply each side
00:10 Substitute appropriate values according to the given data, and solve for AD
00:20 Isolate AD
00:30 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

A parallelogram has a perimeter of 24 cm.

AB = 8

How long is side AD?

888DDDAAABBBCCC

2

Step-by-step solution

Each pair of opposite sides are parallel and equal.

AB is parallel to DC and therefore also AB = DC = 8.

We will use the given perimeter to find AD and BC—which are also equal and parallel to each other.

Let's now calculate the perimeter of the parallelogram:

24=2AB+2AD 24=2AB+2AD

24=16+2AD 24=16+2AD

2416=2AD 24-16=2AD

8=2AD 8=2AD

Then, we'll divide the two sides by 2:

82=2AD2 \frac{8}{2}=\frac{2AD}{2}

AD=4 AD=4

3

Final Answer

4 4

Practice Quiz

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Given the parallelogram:

444222AAABBBDDDCCC

Calculate the perimeter of the parallelogram.

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