Find x in a Parallelogram: Given Perimeter 36 and Side Length 15

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

Because a parallelogram doesn't have four equal sides! It has two pairs of equal opposite sides. So dividing 36 ÷ 4 = 9 would only work for a square, not a parallelogram.

Q: What if I forget the parallelogram perimeter formula?

Remember that opposite sides are equal in a parallelogram. So if you have sides 15 and x, the perimeter is 15 + x + 15 + x, which simplifies to 2(15 + x).

Q: How do I know which sides are opposite in the diagram?

In a parallelogram, parallel sides are equal. Look for sides that don't touch each other - those are opposite sides. The top and bottom sides are equal, and the left and right sides are equal.

Q: What if I get a decimal or fraction for x?

That's perfectly normal! Many geometry problems have non-integer answers. Just make sure to check your arithmetic and verify by substituting back into the perimeter formula.

Parallelogram Properties with Perimeter Calculations

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

00:12 First, let's find X.

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

00:23 The perimeter of a parallelogram is the sum of all its side lengths.

00:41 Substitute the given values to solve for X.

00:44 Move the numbers to one side, and the X terms to the other.

00:54 Now, let's isolate X.

01:08 And that's how we find the solution!

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: Use the perimeter formula for the parallelogram.
Step 2: Substitute the known values and solve for $x$ .

Now, let's work through each step:

Step 1: The formula for the perimeter of a parallelogram is given by:

$P = 2(a + b)$

where $a$ and $b$ are the lengths of the sides. In this case, we have:

$a = 15$ and $P = 36$ .

Step 2: Substitute the values into the perimeter formula:

$36 = 2(15 + x)$

We can simplify this equation to solve for $x$ :

$36 = 30 + 2x$

Step 3: Subtract $30$ from both sides:

$36 - 30 = 2x$

$6 = 2x$

Step 4: Divide both sides by $2$ to solve for $x$ :

$x = \frac{6}{2}$

$x = 3$

Therefore, the solution to the problem is $x = 3$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Perimeter Formula: P = 2(a + b) for opposite sides
Substitution: Replace known values: 36 = 2(15 + x)
Verification: Check P = 2(15 + 3) = 2(18) = 36 ✓

Common Mistakes

Avoid these frequent errors

Adding all four sides individually instead of using the parallelogram formula
Don't write P = 15 + x + 15 + x = wrong setup! This takes longer and increases chance of arithmetic errors. Always use P = 2(a + b) since opposite sides are equal in parallelograms.

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 doesn't have four equal sides! It has two pairs of equal opposite sides. So dividing 36 ÷ 4 = 9 would only work for a square, not a parallelogram.

What if I forget the parallelogram perimeter formula?

Remember that opposite sides are equal in a parallelogram. So if you have sides 15 and x, the perimeter is 15 + x + 15 + x, which simplifies to 2(15 + x).

How do I know which sides are opposite in the diagram?

In a parallelogram, parallel sides are equal. Look for sides that don't touch each other - those are opposite sides. The top and bottom sides are equal, and the left and right sides are equal.

Can x be larger than 15?

Absolutely! There's no rule that says one side must be longer than the other in a parallelogram. As long as opposite sides are equal, any positive value for x is mathematically possible.

What if I get a decimal or fraction for x?

That's perfectly normal! Many geometry problems have non-integer answers. Just make sure to check your arithmetic and verify by substituting back into the perimeter formula.

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