Question

PLEASE HELP DUE SOON PLEASE !!

Answer 1

Answer:

(1 + \sqrt{3} ) : 3

Step-by-step explanation:

AB = x$\sqrt{3} cm$

BC = x cm

Area = l * b = x$\sqrt{3}$ * x

= x^2 $\sqrt{3}$

EFG is equilateral triangle

EF = y cm

Area of triangle = $(\sqrt{3} / 4) * a^{2}$

A = (\sqrt{3} / 4) * y^{2}

As both areas are equal

$\sqrt{3} x^{2} = \sqrt{3} /4 * y^{2}$

$4x^{2} = y^{2}$

2x = y

perimeter of ABCD = 2 (l + b)

$2 (x\sqrt{3} + x)\\= 2x(\sqrt{3} + 1)$

perimeter of EFG = 3y

so ratio is $2x(\sqrt{3} + 1) : 3y$

substitute y = 2x

$2x(\sqrt{3} + 1) : 3*2x\\(\sqrt{3} + 1) : 3$

$(1 + \sqrt{3} ) : 3$