Parallelogram Side Length: Finding CD When Perimeter is 70cm and AB=20cm

Q: Why can't I just divide 70 by 4 to find each side?

That would only work for a square where all sides are equal! In a parallelogram, opposite sides are equal but adjacent sides can be different lengths.

Q: How do I know which sides are opposite?

In parallelogram ABCD, the opposite sides are: AB opposite to CD and BC opposite to DA. They're the sides that don't share a vertex.

Q: Can I use this method for other quadrilaterals?

Only for parallelograms and rectangles (rectangles are special parallelograms). For other quadrilaterals, you need to know more side lengths since opposite sides aren't necessarily equal.

Parallelogram Properties with Perimeter Calculations

A parallelogram has a perimeter of 70 cm.

AB = 20 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

00:13 They are also a pair of opposite sides therefore equal

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

00:29 Let's substitute appropriate values and solve for BD

00:45 Group the numbers into one factor, and BD into one factor

00:54 Isolate BD

01:07 This is the length of BD

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 70 cm.

AB = 20 cm

Calculate side CD.

Step-by-step solution

To solve this problem, we'll use the formula for the perimeter of a parallelogram:

Step 1: Identify the given information:
The perimeter $P$ is 70 cm, and the side $AB = 20$ cm.
Step 2: Apply the perimeter formula:
The formula for the perimeter of a parallelogram is $P = 2(a + b)$ , where $a$ and $b$ are the lengths of adjacent sides.
Step 3: Set up the equation:
Let $CD = x$ . Then, the equation becomes: $70 = 2(20 + x)$
Step 4: Solve for $x$ :
Divide both sides by 2: $35 = 20 + x$ Subtract 20 from both sides: $x = 15$

Therefore, the length of side CD is $15$ cm.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Property: Opposite sides of a parallelogram are equal in length
Formula: Perimeter = 2(adjacent side 1 + adjacent side 2)
Check: AB + BC + CD + DA = 20 + 15 + 20 + 15 = 70 ✓

Common Mistakes

Avoid these frequent errors

Adding all four sides without using parallelogram properties
Don't set up 70 = AB + BC + CD + DA with four unknowns = impossible to solve! This ignores that opposite sides are equal. Always use P = 2(a + b) where a and b are adjacent sides.

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 70 by 4 to find each side?

That would only work for a square where all sides are equal! In a parallelogram, opposite sides are equal but adjacent sides can be different lengths.

How do I know which sides are opposite?

In parallelogram ABCD, the opposite sides are: AB opposite to CD and BC opposite to DA. They're the sides that don't share a vertex.

What if the problem gives me different sides?

The method stays the same! If you know one side length, find its adjacent side using the perimeter formula, then use the property that opposite sides are equal.

Can I use this method for other quadrilaterals?

Only for parallelograms and rectangles (rectangles are special parallelograms). For other quadrilaterals, you need to know more side lengths since opposite sides aren't necessarily equal.

How can I double-check my answer?

Add up all four sides: AB + BC + CD + DA. If it equals the given perimeter, you're correct! Remember: $20 + 15 + 20 + 15 = 70$ ✓

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