If the area of a square is equal to the area of an equilateral triangle, the ratio of the side of the square and the side of the equilateral triangle is

Explanation

Let the side of a square is ‘a’ and side of the equilateral triangle is ‘b’ Now we know that- Area of square = a² Area of a equilateral triangle = $\frac{\sqrt{3}}{4}$b² According to the question- $$ a^2 = \frac{\sqrt{3}}{4}b^2 $$ $$ \frac{a^2}{b^2} = \frac{\sqrt{3}}{4} $$ $$ \frac{a}{b} = \frac{{}^4\sqrt{3}}{2} $$ a: 5 = $3^{\frac{1}{4}}$: 2