Question

The value of the area of an equilateral triangle is irrational. What can you say about the sides of the triangle?

• A. Irrational always
• B. Rational always
• C. Can be either irrational or rational
• D. Integer always

Answer 1

Answer: (C)

Can be either irrational or rational

Area of an equilateral triangle is given by $\frac{\sqrt{3}}{4}{a}^2$. Here, $\sqrt{3}$ is an irrational number. Since, the value of area is irrational, it means $a^2$ can be either rational or irrational. Thus, the length of the sides can be either rational or irrational.