# How do you find the shape of a rectangle of maximum perimeter that can be inscribed in a circle of radius 5 cm?

Define the problem

Look at the figure below:

.

We will find the point

.

.

Perimeter,

In the question here,

.

Therefore, the problem is:

Find

Solution:

We find critical numbers:

Whe

Because

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To find the shape of a rectangle of maximum perimeter inscribed in a circle of radius 5 cm, follow these steps:

- Recognize that the rectangle will be a square when it has the maximum perimeter.
- Determine the diameter of the circle, which is twice the radius, ( d = 2 \times 5 = 10 ) cm.
- The diagonal of the square (and also the diameter of the circle) will be ( d = 10 ) cm.
- Use the properties of a square to find the side length:
- Since all sides of a square are equal, each side length will be half the length of the diagonal, ( \frac{d}{\sqrt{2}} = \frac{10}{\sqrt{2}} ) cm.

- Calculate the side length of the square:
- ( \frac{10}{\sqrt{2}} ) cm ≈ 7.07 cm.

- The shape of the rectangle with maximum perimeter that can be inscribed in the circle of radius 5 cm is a square with side length approximately 7.07 cm.

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