Parallelogram Perimeter: Express in Terms of X When One Side is Double Another

Q: How do I know which side is the longest?

The problem tells us directly that the longest side has length X. Since one side is greater than 2 times another, and X is the longest, we know $ X > 2b $ where b is the shorter side.

Q: Why is the shorter side X/2 and not something else?

When the problem says one side is greater than 2 times another, the standard interpretation for exact solutions is that $ X = 2b $, making $ b = \frac{X}{2} $. This gives us the specific relationship needed.

Q: Do I need to use both pairs of opposite sides?

No! In a parallelogram, opposite sides are equal. So you only need the lengths of two adjacent sides to find the perimeter using $ P = 2(a + b) $.

Q: What if I get a different relationship between the sides?

Always work with the given information carefully. If the problem states a different relationship (like a = 3b), use that instead. The key is identifying which side is longest and expressing the other in terms of X.

Parallelogram Perimeter with Side Relationships

Given a parallelogram in which the length of one side is greater than 2 of the length of another side and given that the length of the longest side is X:

Express by X the perimeter of the parallelogram.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:12 First, express the perimeter of the parallelogram using X.

00:16 Remember, in a parallelogram, opposite sides are equal.

00:29 Notice the longer sides of the parallelogram.

00:39 Let's look at the ratio of the sides based on the given information.

00:46 Let's call side A B as X.

00:50 Next, use X to find the length of side A C.

00:59 Again, opposite sides in a parallelogram are equal, so remember this.

01:04 To find the perimeter, add up all the sides of the parallelogram.

01:16 Now, substitute the values you have and solve to find the perimeter.

01:28 Great job! And that's how we solve this problem.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Given a parallelogram in which the length of one side is greater than 2 of the length of another side and given that the length of the longest side is X:

Express by X the perimeter of the parallelogram.

Step-by-step solution

To solve this problem, we need to calculate the perimeter of the parallelogram using given information. Here are the steps to find the solution:

Step 1: Identify the Longest Side.
The longest side of the parallelogram, denoted by $X$ , is given as $a$ . Therefore, $a = X$ .
Step 2: Determine the Other Side Length.
Given $a > 2b$ , typically $X = 2b$ as a common interpretation for solving problems.
Thus, the other side $b$ is half the longer side: $b = \frac{X}{2}$ .
Step 3: Apply the Perimeter Formula.
The perimeter $P$ of a parallelogram is calculated as $P = 2(a + b)$ .
Plug in the values: $a = X$ , $b = \frac{X}{2}$ .
Thus, perimeter $P = 2\left(X + \frac{X}{2}\right) = 2\left(\frac{2X}{2} + \frac{X}{2}\right) = 2\left(\frac{3X}{2}\right) = 3X$ .

Therefore, the perimeter of the parallelogram in terms of $X$ is $\mathbf{3X}$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Property: Opposite sides of parallelograms are equal in length
Technique: If longest side is X, then shorter side is $\frac{X}{2}$
Check: Perimeter formula P = 2(a + b) gives $2(X + \frac{X}{2}) = 3X$ ✓

Common Mistakes

Avoid these frequent errors

Confusing which side is longest or misunderstanding the relationship
Don't assume the relationship means a = 2b without checking which is larger = wrong perimeter! The problem states one side is greater than 2 times another, so you must identify that the longest side X equals 2b. Always carefully read the given relationships and identify which side is actually longest.

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

How do I know which side is the longest?

The problem tells us directly that the longest side has length X. Since one side is greater than 2 times another, and X is the longest, we know $X > 2b$ where b is the shorter side.

Why is the shorter side X/2 and not something else?

When the problem says one side is greater than 2 times another, the standard interpretation for exact solutions is that $X = 2b$ , making $b = \frac{X}{2}$ . This gives us the specific relationship needed.

Do I need to use both pairs of opposite sides?

No! In a parallelogram, opposite sides are equal. So you only need the lengths of two adjacent sides to find the perimeter using $P = 2(a + b)$ .

What if I get a different relationship between the sides?

Always work with the given information carefully. If the problem states a different relationship (like a = 3b), use that instead. The key is identifying which side is longest and expressing the other in terms of X.

How can I verify my perimeter formula is correct?

Substitute specific numbers! If X = 6, then the shorter side is 3. The perimeter should be $2(6 + 3) = 18$ . Using our formula: $3X = 3(6) = 18$ ✓

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