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

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 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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