Question

proove that area of an equilateral triangle described on one side of of a square is equal to half the area of the equilateral triangle described on one of it's diagonal​

Answer 1

To prove: ar ADE/ar ACF =1/2

Proof: let length of the side of square

           be 'a' cm

          AC^2 = AD^2 +DC^2

          AC^2 = a^2 + a^2

          AC = root2a^2

          AC = root2 ×root a^2

          AC = root2 × a

        Thus, triangle ADE is similar to

          Triangle ACF ( both are

          equilateral triangle )

         Thus, AD/AC = DF/AF = AE/CF

         

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