geometry question..help if possible!?

Question

a square is inscribed in a circle with a radius of 2pie. what is the perimeter of the square?

a. 2 pie (radical 2)

b. 4 pie (radical 2)

c. 6 pie (radical 2)

d. 8 pie (radical 2)

e. 10 pie (radical 2)

Answer 1

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If you draw this, you will see that the diagonals of the square are diameters of the circle.

The square is made up of 2 equal isoceles right triangles whose hypoteneuses are 2* 2pi = 4 pi

If we call he length of the other 2 sides of the triangle (which are 2 sides of the square) x, then from pythogoras, we know that

x^2 + x^2 = (4pi)^2

2x^2 = 16pi^2

x^2 = 8pi^2

x = √(8pi^2

= 2√2 * pi

There are 4 sides, so the perimeter = 8pi√2 - option d

Answer 2

a square is inscribed in a circle with a radius of 2pie. what is the perimeter of the square?

a. 2 pie (radical 2)

b. 4 pie (radical 2)

c. 6 pie (radical 2)

d. 8 pie (radical 2)...... correct answer

e. 10 pie (radical 2)

The diagonal of the inscribed square = twice the radius = 4π

Each side = 2π√2

Perimeter = 4 × 2π√2 = 8π√2

Answer 3

The circle having radius 2pi, the diameter is 4pi, which is the diagonal of the square.

The side of the square is therefor 4pi/(radical 2)= 2pi(radical 2). The perimeter of the square consists of 4 sides and is therefor 8pi(radical 2).

Answer 4

first you need to calculate each length of side of the square.

if you draw from each corner of the square to the center of the circle, you will have 4 right triangles, each with legs of length 2pi, and a hypotenuse of length:

a^2 + b^2 = c^2

2*(2pi)^2 = c^2

c = sqrt(2)*2pi

the hypotenuse is actually the side of each square, which means the perimeter is 4 times the above = 8*pi*sqrt(2), which is answer d.