Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

geometry question..help if possible!?

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)

4 Answers

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  • 1 decade ago
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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

  • 1 decade ago

    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

  • 1 decade ago

    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).

  • 1 decade ago

    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.

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