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

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 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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