The sides of triangle ABC satisfy the relations `a + b - c= 2 and 2ab -c^(2) =4`, then the square of the area of triangle is ______

Answer

3

Explanation

`a + b - c = 2`
and `2ab - c^(2) = 4`
`rArr a^(2) + b^(2) + c^(2) + 2ab - 2bc - 2ca = 4 = 2ab -c^(2)`
`rArr (b-c)^(2) + (a-c)^(2) = 0`
`rArr a = b = c`
Triangle is equilateral, hence
`a = 2`
`rArr Delta = sqrt3`