Question

a square and an equilateral triangle have equal perimeter if the diagonal of the square is 6 root 2 centimetre then find the area of triangle​

Answer 1

Answer:

Step-by-step explanation:

Let the sides of the equilateral triangle be 'a' and the square be 'b'.

As their perimeter is the same, we know 3a=4b.

The diagonal of the square is the hypotenuse of its two sides of lengths b and b.

Hence b^2+b^2=6root(2)$b^{2} +b^{2} =(6\sqrt{2} )^{2}\\2b^{2} =36*2\\b^2=36\\b=6$

As

$4b=3a\\4*6=3*a\\a=24/3\\a=8$

Therefore,

$Area= \frac{ a^2*\sqrt{3} }{4}\\=64*\frac{\sqrt{3}}{4}\\ =16\sqrt{3} units^{2}$