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51. The figure below illustrates an isosceles right
triangle with legs of length 1, along with onefourth of a circle centered at the right-angle
vertex of the triangle. Using the result that
the shortest path between two points is a line
segment, explain why this figure shows that
2(squareroot of 2) <2

  • math -

    I see this is the second time you posted this.
    Of course you realize that we can't see any diagram, but I think I can draw it from your description

    First of all, you must have a typo.
    Did you mean 2√2 < π ??
    Since your statement of2√2 < 2 is false, (2√2 = appr. 2.8)

    In the triangle let the hypotenuse be h
    h^2 = 1^2 + 1^2 = 2
    h = √2

    the arc is (1/4)(2π) = π/2

    then because of the straight between two points is always less than a curve between the same two points,
    √2 < π/2
    multiply by 2
    2√2 < π

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