Calculate Parallelogram Side Length CD Given 45cm Perimeter and AB=15cm

Q: Why don't I need to find all four sides separately?

In a parallelogram, opposite sides are equal! So AB = DC and BC = AD. You only need to find two adjacent sides, then double their sum for the perimeter.

Q: What if I get a decimal answer like 7.5?

Decimal answers are completely normal in geometry! 7.5 cm is the exact length. Just make sure to check your arithmetic and verify with the original perimeter.

Q: How do I know which sides are adjacent?

Adjacent sides share a vertex (corner). In parallelogram ABCD, sides AB and BC are adjacent, as are BC and CD, CD and DA, and DA and AB.

Q: Can I solve this without using the perimeter formula?

The perimeter formula $ P = 2(AB + CD) $ is the most efficient method. Other approaches would be much more complicated and unnecessary for this problem type.

Q: What if the given side was BC instead of AB?

No problem! Since AB = DC and BC = AD in any parallelogram, you'd use the same formula: $ P = 2(BC + CD) $ and solve for the unknown side.

Parallelogram Perimeters with Unknown Sides

A parallelogram has a perimeter of 45 cm

AB = 15 cm

Calculate side CD.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find AC

00:03 Opposite sides are equal in a parallelogram

00:14 They are also a pair of opposite sides therefore equal

00:19 The perimeter of the parallelogram equals the sum of its sides

00:30 Let's substitute appropriate values and solve for AC

00:45 Group the numbers to one factor, and AC to one factor

00:53 Isolate AC

01:09 This is the length of AC

01:14 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A parallelogram has a perimeter of 45 cm

AB = 15 cm

Calculate side CD.

Step-by-step solution

To solve this problem, we will calculate side $CD$ using the perimeter formula of a parallelogram:

The perimeter formula of a parallelogram is $P = 2 \times (AB + CD)$ .
Given $P = 45$ cm and $AB = 15$ cm, substitute these values into the equation: $45 = 2 \times (15 + CD)$ .
Simplify the expression: $45 = 30 + 2 \times CD$ .
Rearrange the equation to solve for $CD$ : $2 \times CD = 45 - 30$ .
This simplifies to: $2 \times CD = 15$ .
Divide both sides by $2$ to find $CD$ : $CD = \frac{15}{2}$ .
Thus, $CD = 7.5$ cm.

Therefore, the length of side $CD$ is $7.5$ cm.

Final Answer

7.5

Key Points to Remember

Essential concepts to master this topic

Rule: Parallelogram perimeter equals 2 times sum of adjacent sides
Technique: Set up equation P = 2(AB + CD), then 45 = 2(15 + CD)
Check: Verify 2(15 + 7.5) = 2(22.5) = 45 cm ✓

Common Mistakes

Avoid these frequent errors

Adding all four sides as if they're different
Don't write P = AB + BC + CD + DA = 15 + BC + CD + 15 = wrong formula! This ignores that opposite sides are equal in parallelograms. Always use P = 2(AB + CD) since AB = DC and BC = AD.

Practice Quiz

Test your knowledge with interactive questions

Find the perimeter of the parallelogram using the data below.

FAQ

Everything you need to know about this question

Why don't I need to find all four sides separately?

In a parallelogram, opposite sides are equal! So AB = DC and BC = AD. You only need to find two adjacent sides, then double their sum for the perimeter.

What if I get a decimal answer like 7.5?

Decimal answers are completely normal in geometry! 7.5 cm is the exact length. Just make sure to check your arithmetic and verify with the original perimeter.

How do I know which sides are adjacent?

Adjacent sides share a vertex (corner). In parallelogram ABCD, sides AB and BC are adjacent, as are BC and CD, CD and DA, and DA and AB.

Can I solve this without using the perimeter formula?

The perimeter formula $P = 2(AB + CD)$ is the most efficient method. Other approaches would be much more complicated and unnecessary for this problem type.

What if the given side was BC instead of AB?

No problem! Since AB = DC and BC = AD in any parallelogram, you'd use the same formula: $P = 2(BC + CD)$ and solve for the unknown side.

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