Question

The sides of a triangle $ABC$ are positive integers. The smallest side has length $l$. What of the following statements is true?

• 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 statements A, B or C above.

Answer 1

Answer: (B)

The area of ABC is always an irrational number.

It has to be an isosceles triangle.
$\Delta =\frac{1}{2}\times 1\sqrt{x^2-\frac{1}{4}}=\frac{1}{4}\sqrt{4x^2-1}$
Perimeter = 1 + 2x $\epsilon$ odd which is always irrational.