Answer:
(1 + \sqrt{3} ) : 3
Step-by-step explanation:
AB = x[tex]\sqrt{3} cm[/tex]
BC = x cm
Area = l * b = x[tex]\sqrt{3}[/tex] * x
= x^2 [tex]\sqrt{3}[/tex]
EFG is equilateral triangle
EF = y cm
Area of triangle = [tex](\sqrt{3} / 4) * a^{2}[/tex]
A = (\sqrt{3} / 4) * y^{2}
As both areas are equal
[tex]\sqrt{3} x^{2} = \sqrt{3} /4 * y^{2}[/tex]
[tex]4x^{2} = y^{2}[/tex]
2x = y
perimeter of ABCD = 2 (l + b)
[tex]2 (x\sqrt{3} + x)\\= 2x(\sqrt{3} + 1)[/tex]
perimeter of EFG = 3y
so ratio is [tex]2x(\sqrt{3} + 1) : 3y[/tex]
substitute y = 2x
[tex]2x(\sqrt{3} + 1) : 3*2x\\(\sqrt{3} + 1) : 3[/tex]
[tex](1 + \sqrt{3} ) : 3[/tex]
