Compare Shapes: Circle (r=5cm) vs Rectangle (side=5cm) Perimeter Challenge

Q: Why can't I just assume the rectangle is a square?

The problem only tells us one side of the rectangle is 5 cm. A rectangle can have different length and width, so we need both measurements to find the perimeter.

Q: What's the circle's circumference with radius 5 cm?

Using $ C = 2\pi r $, we get $ C = 2\pi \times 5 = 10\pi $ cm, which is approximately 31.4 cm.

Q: Could the rectangle ever have the same perimeter as the circle?

Yes! If the rectangle's other side was about $ 5\pi - 5 $ cm (approximately 10.7 cm), then the perimeters would be equal.

Q: How do I know when I have enough information?

For circles: need radius or diameter. For rectangles: need both length and width. For squares: need just one side length.

Q: What if the problem said 'square' instead of 'rectangle'?

Then we'd know both sides are 5 cm! The square's perimeter would be $ 4 \times 5 = 20 $ cm, making the circle larger.

Perimeter Comparison with Missing Dimensions

The radius of a circle is 5 centimeters.

The length of the side of a rectangle is 5 centimeters.

Which shape has a greater perimeter/circumference?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Which shape has a larger perimeter?

00:03 We want to calculate the perimeter of the rectangle

00:09 The perimeter of the rectangle equals twice the sum of adjacent sides

00:17 We only know the length of one side

00:25 Therefore it cannot be determined

00:29 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The radius of a circle is 5 centimeters.

The length of the side of a rectangle is 5 centimeters.

Which shape has a greater perimeter/circumference?

Step-by-step solution

To solve this problem, we'll first calculate the circumference of the circle and then consider the implications for calculating the perimeter of the rectangle:

The formula to calculate the circumference of a circle is:

$C = 2\pi r$

where $r$ is the radius. Given $r = 5$ cm, the circumference of the circle is:

$C = 2\pi \times 5 = 10\pi$ cm

For the rectangle, we need both the lengths to determine its perimeter. Since only one side length of 5 cm is provided and the other is not given or inferable, we cannot determine the rectangle's perimeter precisely.

Therefore, without the missing side length of the rectangle, it is impossible to make a comparison between the two perimeters definitively.

Thus, the correct choice is: Impossible to know.

Final Answer

Impossible to know

Key Points to Remember

Essential concepts to master this topic

Circle Formula: Circumference equals $2\pi r$ where r is radius
Rectangle Formula: Perimeter equals $2(l + w)$ requiring both length and width
Check Information: Verify all necessary measurements are provided before comparing ✓

Common Mistakes

Avoid these frequent errors

Assuming the rectangle is a square
Don't assume the rectangle has equal sides just because one side is 5 cm = wrong comparison! A rectangle needs two different measurements (length and width). Always check that you have all required dimensions before calculating perimeter.

Practice Quiz

Test your knowledge with interactive questions

O is the center of the circle in the diagram.

What is its perimeter?

FAQ

Everything you need to know about this question

Why can't I just assume the rectangle is a square?

The problem only tells us one side of the rectangle is 5 cm. A rectangle can have different length and width, so we need both measurements to find the perimeter.

What's the circle's circumference with radius 5 cm?

Using $C = 2\pi r$ , we get $C = 2\pi \times 5 = 10\pi$ cm, which is approximately 31.4 cm.

Could the rectangle ever have the same perimeter as the circle?

Yes! If the rectangle's other side was about $5\pi - 5$ cm (approximately 10.7 cm), then the perimeters would be equal.

How do I know when I have enough information?

For circles: need radius or diameter. For rectangles: need both length and width. For squares: need just one side length.

What if the problem said 'square' instead of 'rectangle'?

Then we'd know both sides are 5 cm! The square's perimeter would be $4 \times 5 = 20$ cm, making the circle larger.

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