Parallelogram Perimeter: Finding the Total Length When One Side is 0.5X

Q: How do I know which side is longer when I see 0.5X?

The problem states that the larger side is 0.5X. Since one side is 2 times the other, the smaller side must be $ \frac{0.5X}{2} = 0.25X $.

Q: Why do I multiply by 2 in the perimeter formula?

A parallelogram has 4 sides, but opposite sides are equal. So you have 2 sides of length $ 0.5X $ and 2 sides of length $ 0.25X $.

Q: Can I just add 0.5X + 0.25X to get the perimeter?

No! That gives you only two sides. The perimeter is the total distance around, so you need: $ 2(0.5X) + 2(0.25X) = 1.5X $.

Q: What if I got 1X as my answer?

You probably forgot to include both pairs of opposite sides. Remember: $ P = 2(0.5X) + 2(0.25X) = X + 0.5X = 1.5X $, not just $ 0.5X + 0.25X = 0.75X $.

Q: How do I verify my perimeter calculation is correct?

Add all four individual sides: $ 0.5X + 0.25X + 0.5X + 0.25X $. Group the equal sides: $ (0.5X + 0.5X) + (0.25X + 0.25X) = X + 0.5X = 1.5X $ ✓

Parallelogram Perimeter with Variable Expressions

Given a parallelogram in which the length of one side is 2 times the length of the other side and given that the length of the larger side is 0.5X:

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

00:11 Let's express the perimeter of a parallelogram using X.

00:15 Remember, in a parallelogram, opposite sides are equal.

00:26 Now, consider the larger pair of sides.

00:31 Let's look at the side length given in the problem.

00:37 And check the ratio of the sides provided.

00:42 We'll substitute the side value to find the length A C.

00:58 Again, remember that opposite sides are equal in a parallelogram.

01:16 The perimeter is simply the sum of all the sides of the parallelogram.

01:30 Now, substitute the correct values and solve for the perimeter.

01:43 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 2 times the length of the other side and given that the length of the larger side is 0.5X:

Express by X the perimeter of the parallelogram.

Step-by-step solution

To solve the problem, follow these steps:

Step 1: Identify the given side lengths.
The longer side of the parallelogram is given as $0.5X$ . The other side, being half the length of the long side, is $0.25X$ .
Step 2: Use the perimeter formula.
The formula for the perimeter $P$ of a parallelogram is $P = 2a + 2b$ , where $a$ and $b$ are the lengths of the sides.
Step 3: Plug in the side lengths into the formula.
Substitute $a = 0.5X$ and $b = 0.25X$ into the perimeter formula:
$P = 2(0.5X) + 2(0.25X) = X + 0.5X = 1.5X$ .

Thus, the perimeter of the parallelogram expressed in terms of $X$ is $1.5X$ .

Therefore, the correct answer is choice $2$ , which is $1.5X$ .

Final Answer

1.5X

Key Points to Remember

Essential concepts to master this topic

Properties: Opposite sides of parallelograms are equal in length
Formula: Perimeter = 2a + 2b where a and b are adjacent side lengths
Check: Verify by adding all four sides: 0.5X + 0.25X + 0.5X + 0.25X = 1.5X ✓

Common Mistakes

Avoid these frequent errors

Misidentifying which side is longer
Don't assume the 0.5X side is shorter because 0.5 < 1! Since one side is 2 times the other and 0.5X is the larger side, the smaller side must be 0.25X. Always identify the relationship correctly before calculating.

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 longer when I see 0.5X?

The problem states that the larger side is 0.5X. Since one side is 2 times the other, the smaller side must be $\frac{0.5X}{2} = 0.25X$ .

Why do I multiply by 2 in the perimeter formula?

A parallelogram has 4 sides, but opposite sides are equal. So you have 2 sides of length $0.5X$ and 2 sides of length $0.25X$ .

Can I just add 0.5X + 0.25X to get the perimeter?

No! That gives you only two sides. The perimeter is the total distance around, so you need: $2(0.5X) + 2(0.25X) = 1.5X$ .

What if I got 1X as my answer?

You probably forgot to include both pairs of opposite sides. Remember: $P = 2(0.5X) + 2(0.25X) = X + 0.5X = 1.5X$ , not just $0.5X + 0.25X = 0.75X$ .

How do I verify my perimeter calculation is correct?

Add all four individual sides: $0.5X + 0.25X + 0.5X + 0.25X$ . Group the equal sides: $(0.5X + 0.5X) + (0.25X + 0.25X) = X + 0.5X = 1.5X$ ✓

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