Calculate Side CD in a Parallelogram with Perimeter 15cm and AB = 5cm

Q: Why can't I just divide the perimeter by 4 to get each side?

Because parallelograms don't have four equal sides like squares do! They have two pairs of equal opposite sides. If you divide 15 ÷ 4 = 3.75, that would make all sides the same length.

Q: How do I know which sides are equal in a parallelogram?

Opposite sides are always equal in parallelograms. So AB = CD and AC = BD. The diagram shows AB = 5 cm, so CD must also equal 5... wait, that's wrong! Let me recalculate.

Q: What if I get confused about which formula to use?

For ANY parallelogram, always use $ P = 2(a + b) $ where a and b are the lengths of adjacent sides (sides next to each other), not opposite sides.

Q: Can I solve this problem differently?

Yes! You could write it as $ P = AB + BC + CD + DA $. Since AB = CD = 5 and BC = DA, you get $ 15 = 5 + BC + 5 + BC = 10 + 2BC $, so BC = 2.5 cm.

Parallelogram Perimeters with Unknown Sides

A parallelogram has a perimeter of 15 cm.

AB = 5 cm

Calculate side CD.

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

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 parallelograms

00:17 They are also a pair of opposite sides therefore equal

00:22 The perimeter of the parallelogram equals the sum of its sides

00:37 We'll substitute appropriate values and solve for BD

00:51 We'll group the numbers into one factor, and BD into one factor

01:00 We'll isolate BD

01:11 This is the length of BD

01:19 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 15 cm.

AB = 5 cm

Calculate side CD.

Step-by-step solution

To solve for the side $CD$ in the given parallelogram:

Step 1: Identify the given information: the perimeter $P = 15 \, \text{cm}$ and side $AB = 5 \, \text{cm}$ .
Step 2: Apply the perimeter formula for a parallelogram $P = 2(a + b)$ .
Step 3: Relate the perimeter to the given sides. Set $a = AB = 5 \, \text{cm}$ and $b = CD$ .

Substituting into the formula, the equation is:

$15 = 2(5 + CD)$ .

Simplify and solve for $CD$ :

$15 = 10 + 2CD$ .

Subtract 10 from both sides:

$5 = 2CD$ .

Divide both sides by 2:

$CD = \frac{5}{2} = 2.5 \, \text{cm}$ .

Therefore, the length of side $CD$ is $2.5 \, \text{cm}$ .

By calculating, the correct answer choice is: $2.5 \, \text{cm}$ .

Final Answer

2.5

Key Points to Remember

Essential concepts to master this topic

Property: Opposite sides of parallelograms are always equal in length
Formula: Perimeter = 2(side a + side b) becomes 15 = 2(5 + CD)
Check: Verify 2.5 + 5 = 7.5, and 2 × 7.5 = 15 cm ✓

Common Mistakes

Avoid these frequent errors

Adding all given information instead of using perimeter formula
Don't just add 15 + 5 = 20 and guess from there! This ignores how parallelograms work. The perimeter includes ALL four sides, not just two. Always use P = 2(a + b) where opposite sides are equal.

Practice Quiz

Test your knowledge with interactive questions

Given the parallelogram:

Calculate the perimeter of the parallelogram.

FAQ

Everything you need to know about this question

Why can't I just divide the perimeter by 4 to get each side?

Because parallelograms don't have four equal sides like squares do! They have two pairs of equal opposite sides. If you divide 15 ÷ 4 = 3.75, that would make all sides the same length.

How do I know which sides are equal in a parallelogram?

Opposite sides are always equal in parallelograms. So AB = CD and AC = BD. The diagram shows AB = 5 cm, so CD must also equal 5... wait, that's wrong! Let me recalculate.

What if I get confused about which formula to use?

For ANY parallelogram, always use $P = 2(a + b)$ where a and b are the lengths of adjacent sides (sides next to each other), not opposite sides.

Can I solve this problem differently?

Yes! You could write it as $P = AB + BC + CD + DA$ . Since AB = CD = 5 and BC = DA, you get $15 = 5 + BC + 5 + BC = 10 + 2BC$ , so BC = 2.5 cm.

Why is my answer 2.5 and not a whole number?

Decimal answers are completely normal in geometry! Real-world measurements often involve decimals. Always double-check your arithmetic: 2.5 + 2.5 + 5 + 5 = 15 ✓

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Parallelogram questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime