Smile 發問於 科學及數學數學 · 3 月 前

Maths problem, thanks?

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4 個解答

評分
  • 3 月 前
    最佳解答

    △ABC : △ADE = AC : AE

    △ABC : 1 = (AC/AD) : (AE/AD)

    △ABC = (1/cos60°) : cos60°

    △ABC = 2 : 1/2

    △ABC = 4 cm²

    The answer is B.

  • SC147
    Lv 6
    3 月 前

    ∠B=∠E=90⁰

    ∠BAC=30⁰=∠EDA

    ∠BCA=60⁰=∠EAD

    ∴ △ABC ~ △DEA (AAA)

    => area of △ABC :area of △DEA =AC² :DA²

    => area of △ABC :1 = AC² :DA²

    => area of △ABC = (AC/DA)² . . . . . . . . . . . . . . . ①

                   DA

    From rt-angled △ADC, cos 60⁰ = ------

                   AC

                 ½ = DA/AC

             

    From ①: area of △ABC = (2/1)² = 4  (ans : B )

    • SC147
      Lv 6
      3 月 前舉報

      Formula:
      =======
      area of △ABC :area of △XYZ = AB² :XY² (corresponding sides of the 2△s)
      ** In this problem : AC is the hypotenuse of △ABC, while DA is the hypotenuse of △DEA
      ∴ area of △ABC :area of △DEA = AC² :DA²

  • 3 月 前

    △ABC : △ADE = AC : AE

    △ABC : 1 = (AC/AD) : (AE/AD)

    △ABC = (1/cos60°) : cos60°

    △ABC = 2 : 1/2

    △ABC = 4 cm²

    The answer is B.

  • 3 月 前

    △ADE ~ △CAB

    area△ADE : area△ABC = AD ² : AC ² = 1² : 2² = 1 : 4

    4cm²

    B. #

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