Find X in a Parallelogram: Using Perimeter P=54 and Side Length 7

Q: Why can't I just divide the perimeter by 4 to find x?

Because a parallelogram has two different side lengths! If you divide 54 by 4, you get 13.5, which assumes all sides are equal (like a square). In this problem, we have sides of length x and 7.

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

Opposite sides are always equal in a parallelogram. So if one side is x, the opposite side is also x. If another side is 7, its opposite is also 7.

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

Remember: Parallelogram perimeter = 2 × (side 1 + side 2). This works because you're adding each pair of opposite sides once, then doubling it!

Q: Can I solve this without using the perimeter formula?

The perimeter formula $ P = 2(a + b) $ is the most direct method. You could list all four sides (x + 7 + x + 7 = 54), but this takes longer and increases chances for errors.

Parallelogram Perimeter with Unknown Side

Calculate the value of X in the parallelogram below.

P = Perimeter

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 Opposite sides are equal in a parallelogram

00:13 The perimeter of the parallelogram equals the sum of its sides

00:26 Substitute appropriate values and solve for X

00:31 Collect numbers to one side and X terms to the other side

00:38 Isolate X

00:57 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

Calculate the value of X in the parallelogram below.

P = Perimeter

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the known value of one side and the perimeter.
Step 2: Use the perimeter formula to set up an equation.
Step 3: Solve for the unknown side $x$ .

Now, let's work through each step:
Step 1: The problem gives us a perimeter $P = 54$ and one side of the parallelogram as 7.
Step 2: Using the formula for the perimeter of a parallelogram $P = 2(a + b)$ , we have:

$2(x + 7) = 54$

Step 3: Simplify and solve for $x$ :

Divide both sides by 2:

$x + 7 = 27$

Subtract 7 from both sides to isolate $x$ :

$x = 27 - 7$

Simplifying, we obtain:

$x = 20$

Therefore, the solution to the problem is $x = 20$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Perimeter Formula: P = 2(a + b) for opposite sides
Substitution: Replace P = 54 and one side = 7 into formula
Verification: Check 2(20 + 7) = 54 to confirm x = 20 ✓

Common Mistakes

Avoid these frequent errors

Using P = 4x instead of P = 2(x + 7)
Don't assume all sides are equal = treating parallelogram like square! This ignores that parallelograms have two pairs of equal sides, not four equal sides. 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 the perimeter by 4 to find x?

Because a parallelogram has two different side lengths! If you divide 54 by 4, you get 13.5, which assumes all sides are equal (like a square). In this problem, we have sides of length x and 7.

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

Opposite sides are always equal in a parallelogram. So if one side is x, the opposite side is also x. If another side is 7, its opposite is also 7.

What if I get confused about which formula to use?

Remember: Parallelogram perimeter = 2 × (side 1 + side 2). This works because you're adding each pair of opposite sides once, then doubling it!

Can I solve this without using the perimeter formula?

The perimeter formula $P = 2(a + b)$ is the most direct method. You could list all four sides (x + 7 + x + 7 = 54), but this takes longer and increases chances for errors.

How do I check if x = 20 is really correct?

Substitute back: If x = 20, then the sides are 20, 7, 20, 7. Adding them: 20 + 7 + 20 + 7 = 54 ✓ This matches the given perimeter!

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