Question

If the area of square is (7+2 root12) square units then find its side and perimeter.

Answer 1

area of square = 7 +2√12 = (7 +4√3 ) unit^2

let side length is x


we know,

area of square =(side length)^2
7 + 4√3 = x^2

4 +3 +2.√4.√3 =x^2

here we see this is same as (a +b)^2 formula ,

so,. (√4 +√3)^2 =x ^2

take square root both sides

x = +_( 2 + √3)

but length is not negative so,

x = ( 2 + √3) unit

now ,
perimeter of square = 4 × side length
= 4 × (2 +√3) unit
= (8 + 4√3 ) unit