The area of ​​a triangular field with equal sides is 3√3 times the area of ​​a parallelogram shaped park whose adjacent sides are 30 m and 40 m and the length of one diagonal is 50 m. What is the perimeter of the triangular field?

Area of triangular field = 3√3 times the area of a parallelogram,   adjacent sides of parallelogram are 30 m and 40 m and the length of one diagonal of parallelogram 50 m

​Area of parallelogram =2×area  of triangle​

Area of triangle where three sides a, b, c are given is $$\sqrt{s(s−a)(s−b)(s−c)}$$​  where  $$S = \frac{a + b + c }{2}$$ 

 $$S = \frac{30 + 40 + 50}{2}$$  = 60 = $$\sqrt{60(60−30)(60−40)(60−50)} = \sqrt{60\times 30\times 20\times10}$$   = 600

Area of parallelogram = $$2\times 600 = 1200$$ 

According to the question 

Let the side of equilateral triangle = a 

Area of triangular field = 3√3 times the area of a parallelogram