Question

Which of the following is(are) true in the case of equilateral triangles?

• A. The area is inversely proportional to the square of the length of a side.
• B. The square root of area is directly proportional to the length of a side.
• C. The area is directly proportional to the length of a side.
  
• D. The area is directly proportional to the square of the length of a side.

Answer 1

Answer: (B), (D)

The correct options are
B The square root of area is directly proportional to the length of a side.
D The area is directly proportional to the square of the length of a side.

Area of an equilateral triangle is $\text{A}=\frac{\sqrt{3}}{4}{a}^2$ where a is the side of the triangle.
Thus, Area ∝ square of the length of a side, with constant of proportionality $\frac{\sqrt{3}}{4}$.
Also, $\sqrt{A}rea\propto \text{Length of a side}$