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    Question

    The area of an isosceles triangle ABC is 8√5 cm

    2 . If AB = BC and AC = 8 cm, then find the perimeter of triangle ABC.
    A 16 cm Correct Answer Incorrect Answer
    B 18 cm Correct Answer Incorrect Answer
    C 20 cm Correct Answer Incorrect Answer
    D 12 cm Correct Answer Incorrect Answer

    Solution

    Let AB = BC = 'x' cm

    Area of isosceles triangle = {(c/4) X √(4a 2  - c 2 )} [Where 'a' is the length of two equal sides and 'c' is the length of third (unequal) side]

    8√5 = (8/4) X {√(4 X x 2  - 8 2 )}

    Or, (4√5) = √(4x 2  - 64)

    Squaring both sides.

    (16 X 5) = 4x 2  - 64

    Or, 144 = 4x 2

    Or, x 2  = 36

    So, x = 6 cm (Since, length cannot be negative therefore, we will take the positive root only)

    So, required perimeter = 6 + 6 + 8 = 20 cm

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