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A square and an equilateral triangle have the same perimeter. If the diagonal of the square is 12√5 cm, then find the altitude of equilateral triangle.

Let side of the square be a cm so, a√2 = 12√5 so a = 12√5/√2 4a = 48√5/√2 4a is the perimeter of the square as well as the triangle so side of the equilateral triangle = 4a/3 = 16√5/√2 so altitude of the equilateral triangle is √3/2 × side = 16√15/√8

Let the side of square= xcm x√2= 12√5 x=12√5/2 4x= perimeter of square= perimeter of triangle 4×12√5/2= perimeter of triangle [substituting x] 2×12×√2×√5= perimeter of triangle now simplify and find the answer