Rectangle Perimeter Equation: Solving for X when X+2 and X are Adjacent Sides (30cm)

Q: Why do we need to add all four sides for the perimeter?

Perimeter means the distance around the entire shape! A rectangle has 4 sides, so we must add: length + width + length + width. Since opposite sides are equal, we get $ 2 \times \text{length} + 2 \times \text{width} $.

Q: How do I know which side is x and which is x+2?

It doesn't matter! The problem says one side is 2 cm longer than the adjacent side. You can call the shorter side x and the longer side x+2. The math works the same way.

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

Absolutely! That's actually cleaner: $ 30 = 2(x+2) + 2x $. Distribute to get $ 30 = 2x + 4 + 2x = 4x + 4 $, which is the same equation!

Q: What if I get a decimal answer for a length?

Decimal lengths are perfectly normal in geometry! 6.5 cm is a valid measurement. Always check that your answer makes sense - is it positive? Does it give the correct perimeter?

Rectangle Perimeter with Variable Side Lengths

A rectangle has a perimeter measuring 30 cm.

One side of the rectangle is 2 cm longer than the adjacent side.

Calculate the length of the rectangle's shorter sides.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the shorter side of the rectangle

00:03 The side according to the given data

00:08 In a rectangle, opposite sides are equal

00:19 The length of the side according to the given data

00:22 In a rectangle, opposite sides are equal

00:29 The perimeter of the rectangle equals the sum of its sides

00:39 Insert the appropriate values into the formula according to the given data and solve for X

00:55 Collect like terms

01:04 Isolate X (the small side)

01:14 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

A rectangle has a perimeter measuring 30 cm.

One side of the rectangle is 2 cm longer than the adjacent side.

Calculate the length of the rectangle's shorter sides.

Step-by-step solution

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

$AB=CD=x+2$

$AD=BC=x$

We can then create the following equation based on the given data:

$30=x+x+2+x+x+2$

$30=4x+4$

$30-4=4x$

$26=4x$

$x=6.5$

Final Answer

$6.5$

Key Points to Remember

Essential concepts to master this topic

Perimeter Formula: Rectangle perimeter equals twice length plus twice width
Setup Equation: $30 = 2(x+2) + 2x$ or $30 = 4x + 4$
Verification: Check that 6.5 + 8.5 + 6.5 + 8.5 = 30 cm ✓

Common Mistakes

Avoid these frequent errors

Writing the perimeter equation incorrectly
Don't write $30 = x + (x+2)$ = wrong equation! This only adds two sides instead of all four sides of the rectangle. Always remember that perimeter includes all four sides: $30 = x + (x+2) + x + (x+2)$ .

Practice Quiz

Test your knowledge with interactive questions

Calculate the perimeter of the rectangle below.

FAQ

Everything you need to know about this question

Why do we need to add all four sides for the perimeter?

Perimeter means the distance around the entire shape! A rectangle has 4 sides, so we must add: length + width + length + width. Since opposite sides are equal, we get $2 \times \text{length} + 2 \times \text{width}$ .

How do I know which side is x and which is x+2?

It doesn't matter! The problem says one side is 2 cm longer than the adjacent side. You can call the shorter side x and the longer side x+2. The math works the same way.

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

Absolutely! That's actually cleaner: $30 = 2(x+2) + 2x$ . Distribute to get $30 = 2x + 4 + 2x = 4x + 4$ , which is the same equation!

What if I get a decimal answer for a length?

Decimal lengths are perfectly normal in geometry! 6.5 cm is a valid measurement. Always check that your answer makes sense - is it positive? Does it give the correct perimeter?

How can I double-check my work?

Substitute your answer back: if x = 6.5, then the sides are 6.5 cm and 8.5 cm. Check: $2(6.5) + 2(8.5) = 13 + 17 = 30$ ✓

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Rectangle Perimeter Equation: Solving for X when X+2 and X are Adjacent Sides (30cm)

Rectangle Perimeter with Variable Side Lengths

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why do we need to add all four sides for the perimeter?

How do I know which side is x and which is x+2?

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

What if I get a decimal answer for a length?

How can I double-check my work?

🌟 Unlock Your Math Potential

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