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.

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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 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

Find the perimeter of the parallelogram using the data below.

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 ✓

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