A square and an equilateral triangle have equal perimeters. If the diagonal of the square is `12sqrt(2)\ c m` , then area of the triangle is:
`24sqrt(2)\ c m^2`
(b) `24sqrt(3)\ c m^2`
`48sqrt(3)\ c m^2`
(d) `64sqrt(3)\ c m^2`

Explanation

Diagonal of a square =12`sqrt2` cm
Side if square= `2(DC)^2` = (12`sqrt2`)
`2(DC)^2`= `144xx2/2` = DC= 12 cm
Perimeter of square = 4(12) cm = 48 ​cm
Perimeter of equilateral triangle = 3a ( where a is side of the triangle)
`a= 48/3= 16` cm
Area of equilateral triangle is `(sqrt3/4)a^2`
`(sqrt3/4)xx16^2`
`64sqrt3 cm^2`
Hence, option (d) is correct.