Solve for X: Rectangle Perimeter 26 with Sides (X+2) and (X+3)

Q: Why do I need to add all four sides instead of just two?

The perimeter is the total distance around the shape! Even though opposite sides are equal, you still need to count all four sides when calculating the total perimeter.

Q: How do I know which sides are equal in a rectangle?

In any rectangle, opposite sides are always equal. So if one side is (x+2), the side across from it is also (x+2). Same for the other pair!

Q: Can I use the formula P = 2l + 2w instead?

Absolutely! That's actually cleaner: P = 2(x+3) + 2(x+2) = 2x + 6 + 2x + 4 = 4x + 10. Both methods give the same result.

Rectangle Perimeter with Variable Side Expressions

Look at the following rectangle:

The perimeter of the rectangle is 26.

Calculate the value of X.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the value of X

00:05 Opposite sides are equal in a rectangle

00:26 The perimeter of the rectangle equals the sum of its sides

00:39 Substitute in the relevant values according to the given data and solve for X

01:06 Collect like terms

01:22 Isolate X

01:36 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the following rectangle:

The perimeter of the rectangle is 26.

Calculate the value of X.

Step-by-step solution

Since in a rectangle every pair of opposite sides are equal, we can claim that:

$AD=BC=x+2$

$AB=CD=x+3$

Since the perimeter of the rectangle is equal to 26, we can substitute the data into the formula:

$26=x+2+x+3+x+2+x+3$

$26=4x+10$

$26-10=4x$

$16=4x$

Let's divide both sides by 4:

$4=x$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rectangle Property: Opposite sides are equal, so use formula P = 2(length + width)
Technique: Combine like terms: (x+2) + (x+3) + (x+2) + (x+3) = 4x + 10
Check: Substitute x = 4: P = 2(6 + 7) = 26 ✓

Common Mistakes

Avoid these frequent errors

Adding sides incorrectly as 2x + 5
Don't just add the expressions once and multiply by 2 = P = 2(2x + 5) = 4x + 10 gives wrong setup! You're missing that the rectangle has FOUR sides total. Always add all four sides: (x+2) + (x+3) + (x+2) + (x+3) = 4x + 10.

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle ABCD below.

Side AB is 6 cm long and side BC is 4 cm long.

What is the area of the rectangle?

FAQ

Everything you need to know about this question

Why do I need to add all four sides instead of just two?

The perimeter is the total distance around the shape! Even though opposite sides are equal, you still need to count all four sides when calculating the total perimeter.

How do I know which sides are equal in a rectangle?

In any rectangle, opposite sides are always equal. So if one side is (x+2), the side across from it is also (x+2). Same for the other pair!

What if I get a negative value for x?

Check your work! Since x represents part of a side length, it should be positive. Negative values usually mean there's an error in your equation setup or solving.

Can I use the formula P = 2l + 2w instead?

Absolutely! That's actually cleaner: P = 2(x+3) + 2(x+2) = 2x + 6 + 2x + 4 = 4x + 10. Both methods give the same result.

How do I check if my rectangle makes sense?

After finding x = 4, calculate the actual side lengths: one pair is 6 units, the other is 7 units. These are positive and reasonable for a rectangle!

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