The sides of a triangle ABC are positive integers. The smallest side has length 1. Which of the following statement is true ?

Options

A. The area of ABC is always a rational number
B. The area of ABC is always an irrational number
C. The perimeter of ABC is an even integer
D. The information provided is not sufficient to conclude any of the statement A, B or C above

Answer

B

Explanation

`1+b gt c rArr c-b lt 1`
`a+c gt b rArr b-c lt 1`
`-1 lt b-c lt 1`
b, c are integers so `b-c=0 rArr b=c`
semi perimeter` S=(2b+1)/(2) = b+(1)/(2)`
area `sqrt((b+(1)/(2))(b+(1)/(2)-b)(b+(1)/(2)-c)((b)/(2)+(1)/(2)-1))=(1)/(2) sqrt(b^(2)-(1)/(4))` = Irrational