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9th Class Mathematics Triangles Question Bank Triangle

  • question_answer
    In the given figure below, \[\Delta \mathbf{ABC}\] is an isosceles triangle with \[\mathbf{AB}=\mathbf{AC}=\mathbf{17}\]cm and altitude from A to BC is 15 cm. The length of side BC is:

    A)  9 cm                           

    B)  12 cm         

    C)  16 cm   

    D)  20 cm

    Correct Answer: C

    Solution :

    (c): \[AB=AC=17\]cm, \[AD\bot BC;AD=15\]cm \[\therefore \] \[BD=DC\] In \[\Delta ABD\] \[BD=\sqrt{A{{B}^{2}}-A{{D}^{2}}}\] \[BD=\sqrt{{{17}^{2}}-{{15}^{2}}}\] = 8 cm \[\therefore \] \[BC=2\times BD=2\times 8\] = 16 cm.                      


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