Question

The sequence of the area of the equilateral triangles having sides 1 cm, 2 cm, 3 cm ___is

• A. $\frac{\sqrt{3}}{2},\sqrt{3},2\sqrt{3}$
• B. $\frac{\sqrt{3}}{4},\sqrt{3},\frac{9\sqrt{3}}{4}$
• C. $\sqrt{3},\frac{9\sqrt{3}}{4}$
• D. $2\sqrt{3},3\sqrt{3},4\sqrt{3}$

Answer 1

The correct option is B

$\frac{\sqrt{3}}{4},\sqrt{3},\frac{9\sqrt{3}}{4}$

Area of an equilateral triangle =$\frac{\sqrt{3}}{4}{a}^2$ (where a =side of the triangle)

$\therefore$ Area of triangle with sides 1 cm $=\frac{\sqrt{3}}{4}(1{)}^2=\frac{\sqrt{3}}{4}$ units.

$\therefore$ Area of triangle with side 2 cm $=\frac{\sqrt{3}}{4}(2{)}^2=\sqrt{3}$ units.

$\therefore$ Area of triangle with side 3 cm $=\frac{\sqrt{3}}{4}(3{)}^2=\frac{9\sqrt{3}}{4}$ units.

$\therefore$ Sequence is $\frac{\sqrt{3}}{4},\sqrt{3},\frac{9\sqrt{3}}{4}$