• The area of an isosceles \( \Large \triangle ABC \) with AB = AC and altitude AD = 3 cm is 12 sq cm. What is its perimeter?

    A) 18 cm

      B) 16 cm

    C) 14 cm

      D) 12 cm

    Correct Answer:
    A) 18 cm

    Description for Correct answer

    Let AB = CA = a cm and base = b cm

    Now, area of the \( \Large \triangle ABC \)= \( \Large \frac{1}{2}\times b\times h \)

    => 12= \( \Large \frac{1}{2}\times b\times 3 \)


    b= \( \Large \frac{12\times 2}{3} \)=8cm

    Here, BD=CD=\( \Large \frac{b}{2}=\frac{8}{2} \)=4cm

    In right angled \( \Large \triangle ABD \) , by Pythagoras theorem,

    AB=\( \Large \sqrt{BD^{2}+AD^{2}} \) => a=\( \Large \sqrt{4^{2}+3^{2}} \)

    =\( \Large \sqrt{16+9}=\sqrt{25} \)=5cm

    Now, perimeter of an isosceles triangle

    = 2a + b = \( \Large 2\times 5+8 \)

    = 10 + 8 = 18 cm

     


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