What will be the Each Side of the Triangle ? If

On decreasing each side of an equilateral triangle by  2 cm, there is a decrease of 4√3 cm square in its area. The length of each side of the triangle is

  1. 6cm
  2. 8cm
  3. 3cm
  4. 5cm
Manish Listener Asked on 15th June 2015 in Maths.
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  • 1 Answer(s)

    Answer: (4) 5 cm
    Explanation:-
    Let be the side of a equilateral triangle = a cm
    Then, the area of a equilateral triangle = √3a2/4
    Side is decreased by 2 cm
    Then, the  side = (a – 2) cm
    The new area of triangle = √3(a- 2)2/4
    According to the question,
    √3a2/4 – √3(a- 2)2/4 = 4√3
    a2 – (a – 2)2 = 4 x 4
    a2 – a2 – 4 + 4a = 16
    4a = 16 + 4 = 20
    a = 20/4
    a = 5

    Hence, the answer is (4) 5 cm.

    Anurag Mishra Professor Answered on 15th June 2015.
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