Question

Area of an equilateral triangle is $4\sqrt{3}$ sq.cm. Then the length of the diagonal of a square whose side is equal to the height of the equilateral triangle, (in cm) is

Answer 1

Area of equilateral triangle $=\frac{\sqrt{3}}{4}{a}^2$

$\Rightarrow 4\sqrt{3}=\frac{\sqrt{3}}{4}{a}^2$

$\Rightarrow 16\sqrt{3}=\sqrt{3}{a}^2$

$\Rightarrow a^2=16$

$\Rightarrow a=\sqrt{16}$

$\Rightarrow a=4cm$

Hence length of the diagonal of the square is 4 cm