9th Class Mathematics Triangles Question Bank Triangle

  • question_answer
    If each side of triangle ABC is of length 4 and if AD is 1 and \[\mathbf{ED}\bot \mathbf{AB}\]. The area of region BCED is equal to

    A)  \[8\sqrt{3}\]                 

    B)  \[4\sqrt{3}\]

    C)  \[4.5\sqrt{3}\]              

    D)  \[3.5\sqrt{3}\]

    Correct Answer: D

    Solution :

    (d) Area of ABC will be \[\frac{\sqrt{3}}{4}{{\left( 4 \right)}^{2}}=4\sqrt{3}\] ADE is right triangle where AD =1, so we will bet \[DE=\sqrt{3}\]and \[AE=2\] So area of \[\Delta ADE\] will be \[\frac{1}{2}\times 1\times \sqrt{3}=\frac{\sqrt{3}}{2}\] So area of BCDE = \[4\sqrt{3}-\sqrt{3}/2=3.5\sqrt{3}\]


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