Find X in Rectangle: Solving with Perimeter of 18 and Side Length 3

Q: Why do we write X twice in the perimeter equation?

In a rectangle, opposite sides are always equal. Since X represents one side length, the opposite side must also be X. That's why we get X + X + 3 + 3 = 18.

Q: What if I set up the equation as 2X + 2(3) = 18?

That's actually perfect! Using the formula P = 2l + 2w gives the same result. Both methods work: X + X + 3 + 3 or 2X + 6 equals 18.

Q: What if I get X = 6 but one of the answer choices is 12?

Be careful not to confuse X with the total length of both X-sides! X = 6 is one side length, while 2X = 12 is the combined length of both X-sides.

Rectangle Perimeter with Variable Sides

If the rectangle below has a perimeter of 18.

Calculate X using the given data:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:08 Let's find the value of X.

00:11 Use the formula for the perimeter of a rectangle. That's two times the sum of its sides.

00:18 Now, put in the numbers from the problem. Solve for X.

00:22 Distribute the terms. Multiply each factor carefully.

00:32 Solve the multiplications one by one. Then add them up.

00:38 Next, we need to isolate X.

00:46 And that's how we solve the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

If the rectangle below has a perimeter of 18.

Calculate X using the given data:

Step-by-step solution

Since we are given the perimeter, and in a rectangle opposite sides are equal, let's add up all the sides:

$X+X+3+3=18$

$X+X+6=18$

$2X=18-6$

$2X=12$

Let's divide both sides by 2:

$X=6$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Perimeter Formula: For rectangles, add all four sides together
Technique: Group like terms: X + X + 3 + 3 = 2X + 6
Check: Substitute X = 6: 6 + 6 + 3 + 3 = 18 ✓

Common Mistakes

Avoid these frequent errors

Not recognizing opposite sides are equal
Don't assume all four sides are different = overcomplicated setup! This leads to confusion about which sides match. Always remember that in rectangles, opposite sides are equal in length.

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle below.

Side DC has a length of 1.5 cm and side AD has a length of 9.5 cm.

What is the perimeter of the rectangle?

FAQ

Everything you need to know about this question

Why do we write X twice in the perimeter equation?

In a rectangle, opposite sides are always equal. Since X represents one side length, the opposite side must also be X. That's why we get X + X + 3 + 3 = 18.

What if I set up the equation as 2X + 2(3) = 18?

That's actually perfect! Using the formula P = 2l + 2w gives the same result. Both methods work: X + X + 3 + 3 or 2X + 6 equals 18.

How do I know which side is X and which is 3?

Look at the diagram carefully! The problem shows that one pair of opposite sides has length 3, so the other pair must have length X.

Can X be smaller than 3?

In this problem, no! Since the perimeter is 18 and we have two sides of length 3 each, the remaining length (2X) must be 18 - 6 = 12, making X = 6.

What if I get X = 6 but one of the answer choices is 12?

Be careful not to confuse X with the total length of both X-sides! X = 6 is one side length, while 2X = 12 is the combined length of both X-sides.

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