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

$$ 100+5-100+5 $$

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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