A square and equilateral triangle have equal perimeters. If the diagonal of the square is 12 cm, find the area of triangle.

The correct answer is: 110.85 cm2

It is given that diagonal of the square = 12 cm
Using Pythagoras theorem in triangle ACD
AD² = AC² + CD²
(12)² = x² + x² = 2x²
288 = 2x²
144 = x²
12 = x
So, side of the square = 12 cm
Let side of an equilateral triangle = a
Perimeter of triangle = Perimeter of square
⇒ 3a  =  4(side) = 4(12) = 48 cm
⇒ a = 16 cm
Now, Area of an equilateral triangle =  a²
=  16² = 64
( = 1.73)
= 110.85 cm²