Solve for X: Parallelogram with Perimeter 42 and Side Length x+1

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

A parallelogram has 4 sides, but opposite sides are equal! So if adjacent sides are x and x+1, you have two sides of length x and two of length x+1. That's why P = 2(x + (x+1)).

Q: Can I solve this without setting up an equation?

You could guess and check, but setting up $ 42 = 2(x + (x+1)) $ is much faster and more reliable. Algebra gives you the exact answer every time!

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

Adjacent sides are sides that share a vertex (corner). In any parallelogram, you only need to know two adjacent side lengths because opposite sides are always equal.

Q: What if the problem gave me the area instead of perimeter?

That would be a completely different problem! Area uses multiplication (base × height), while perimeter uses addition (sum of all sides). Always read carefully to see what's given.

Parallelogram Perimeter with Variable Sides

Calculate 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

00:14 The perimeter of the parallelogram equals the sum of its sides

00:28 Substitute appropriate values and solve for X

00:35 Group the numbers to one side, and X terms to one side

00:45 Isolate X

01:03 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate X in the parallelogram below.

P = Perimeter

Step-by-step solution

To solve this problem, we'll follow these steps to find $x$ :

Step 1: Use the formula for the perimeter of a parallelogram.
Step 2: Set up an equation involving $x$ and solve for $x$ .
Step 3: Substitute the values and perform calculations to find $x$ .

Let's proceed:

Step 1: The formula for the perimeter of a parallelogram is:
$P = 2(a + b)$ where $a$ and $b$ are the lengths of two adjacent sides. Here, $a = x$ and $b = x+1$ .

Step 2: According to the problem, the perimeter $P = 42$ . Therefore, we set up the equation:
$42 = 2(x + (x + 1))$

Step 3: Simplify and solve for $x$ :
$42 = 2(2x + 1)$
$42 = 4x + 2$
Subtract 2 from both sides:
$40 = 4x$
Solve for $x$ by dividing both sides by 4:
$x = 10$

Therefore, the solution to the problem is $x = 10$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Parallelogram perimeter equals twice sum of adjacent sides
Technique: Set up equation $42 = 2(x + (x+1))$ then simplify
Check: Substitute x = 10: sides are 10 and 11, perimeter = 2(10+11) = 42 ✓

Common Mistakes

Avoid these frequent errors

Adding sides incorrectly in perimeter formula
Don't use P = x + (x+1) = 2x + 1 for perimeter! This only counts each side once, giving P = 21 instead of 42. Always remember a parallelogram has 4 sides: use P = 2(side₁ + side₂).

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 do we multiply by 2 in the perimeter formula?

A parallelogram has 4 sides, but opposite sides are equal! So if adjacent sides are x and x+1, you have two sides of length x and two of length x+1. That's why P = 2(x + (x+1)).

What if I get a negative answer for x?

Check your algebra! In this problem, x represents a side length, so it must be positive. If you get negative, you likely made an error in solving the equation.

Can I solve this without setting up an equation?

You could guess and check, but setting up $42 = 2(x + (x+1))$ is much faster and more reliable. Algebra gives you the exact answer every time!

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

Adjacent sides are sides that share a vertex (corner). In any parallelogram, you only need to know two adjacent side lengths because opposite sides are always equal.

What if the problem gave me the area instead of perimeter?

That would be a completely different problem! Area uses multiplication (base × height), while perimeter uses addition (sum of all sides). Always read carefully to see what's given.

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