Question

a regular polygon, with number of diagonals equal to 9, is inscribed inside a circle, which in turn is inscribed inside a square of area 100 square units. Find the ratio of the craumference of polygon, circle and square​

Answer 1

Answer:

please make me BRAINLIST

Answer 2

Polygon

Given:

A polygon having 9 diagonals , it is inscribed in a circle, circle is inscribed in square of area 100 square units.

To find:

Ration of circumference of polygon, circle and square.

Steps by step explanation:

I have attached the figure depicting these conditions,

As the number of diagonals of polygon is 9 , so according to the formula:

$no. of diagonals=\frac{n(n-3)}{2}$

where n is no. of sides in polygon.

Number of sides will be 6 in regular polygon if no. of diagonals are 9.  

As the area of square is 100 square units then , sides of square will be of 10 units by the formula,

area of square = $sides^{2}$

So, radius of circle will be 5 units as show in figure b.

And the angle that hexagon will make is 60° at the center, and hence it will form equilateral triangle of side 5 units.

So, sides of regular hexagon is 5 units.

So ratio of perimeter of polygon, circumference of circle and perimeter of square will be

$6(sides ): 2\pi(radius ):4(square's side)$

$6(5): 2\pi(5):4(10)$

$30:10\pi:40\\3:\pi:4$

Hence the required ratio is $3:\pi:4$