Rectangle Inscribed In Circle

mathxyz · 2024-04-27 07:17:43

A rectangle is Inscribed in a circle of radius 2.
Let P = (x, y) be a point in quadrant 1 that is a vertex of the rectangle and is on the circle.

A. Express the area A of the rectangle as a function of x.

B. Express the perimeter p of the rectangle as a function of x.

Let me see.

Part A

We want A(x).
Area of square = (side)^2.
Perimeter of square = 4(side), where side is x.

A(x) = (perimeter of square of length x)^2(something)

A(x) = (4x)(something)

I need help finding "something" for A(x).

Part B

In quadrant 1 we have a square of length x.

We want P(x).

Length of side of square in quadrant 1 = x.

Perimeter of square = 4(side).

P(x) = 4x + 4(something)

I need finding "something" for P(x).

Last edited by mathxyz (2024-04-27 07:53:56)

Bob · 2024-04-27 19:38:45

It's a rectangle not a square.

Bob

mathxyz · 2024-04-28 01:21:43

Bob wrote:

It's a rectangle not a square.
Bob

The entire image is a rectangle but we are in quadrant 1. The image in quadrant 1 is a little square.

Bob · 2024-04-28 04:16:13

Sorry but it isn't. The corner is (x,y) so unless x=y the length and width are different.

Bob

mathxyz · 2024-04-28 04:36:48

Bob wrote:

Sorry but it isn't. The corner is (x,y) so unless x=y the length and width are different.
Bob

Thank you. I will return to the beginning of this section because I obviously did not learn a thing.

Math Is Fun Forum