Question

The area of an equilateral triangle is 2 root 3 cm square. What is its semi-perimeter?

Answer 1

area of equilateral ∆=(√3/4)*side*side
putting the values we get side as 2√2 cm
then ,semi perimeter=1/2*3*2√2
which is 3√2 cm

Answer 2

The Semi - Perimeter of equilateral triangle is $\bold{3 \sqrt{2}\ \mathrm{cm}}$

Given:

Area of equilateral triangle$= 2 \sqrt{3}\ \mathrm{cm}^{2}$

To find:

The Semi - Perimeter of equilateral triangle

Solution:

We know, for an equilateral triangle,

Area of the equilateral $\Delta=\frac{\sqrt{3}}{4} a^{2}$

Where a = side of the triangle  

Given area of equilateral $\Delta=2 \sqrt{3}\ \mathrm{cm}^{2}$

$\frac{\sqrt{3}}{4} a^{2}=2\ \sqrt{3} c m^{2}$

$a^{2}=\frac{2 \sqrt{3} \times 4}{\sqrt{3}}\ \mathrm{cm}^{2}$

$\begin{aligned} a^{2} &=2 \times 4\ \mathrm{cm}^{2} \\ a &=\sqrt{2 \times 4\ \mathrm{cm}^{2}} \\ & a=2 \sqrt{2}\ \mathrm{cm} \end{aligned}$

Thus, each side of equilateral triangle  $=2 \sqrt{2}\ \mathrm{cm}$

∴ Perimeter of equilateral triangle $=3 \times a=3 \times 2 \sqrt{2}\ \mathrm{cm}=6 \sqrt{2}\ \mathrm{cm}$

∴ Semi - Perimeter of the equilateral triangle $=\frac{6 \sqrt{2}}{2}\ c m=3 \sqrt{2}\ c m$