Question

If the area of an equilateral triangle is 2 √3 square cm , then its semi perimeter will be :

(a) 2√2 cm

(b) 3√2 cm

(c) 4√2 cm

(d) √2 cm​

Answer 1

(b) 3√2 cm is correct answer

Explaination:-

Area of equilateral triangle with side "a" is given by

$\qquad\qquad\boxed{ \rm Area = \dfrac{\sqrt{3}a^2}{4}}$

Using this formula, we will find out the side of the equilateral triangle.

Given that, area is 2√3 , hence,

$\sf\dfrac{\sqrt{3}a^2}{4} = 2\sqrt{3}$

$\sf\dashrightarrow a = \sqrt{ \dfrac{2\sqrt{3} \times 4}{\sqrt{3}}}$

$\sf\dashrightarrow a = \sqrt{8}cm = 2\sqrt{2}cm$

Side of the equilateral triangle = a = 2√2

Perimeter of the equilateral with a side "a" is given by

$\qquad\qquad\boxed{\rm Perimeter= 3a}$

Therefore, semi-perimeter will be

$\dfrac{3a}{2}$

a =2√2cm

$\sf\dfrac{3(2\sqrt{2}cm)}{2} = 3\sqrt{2}cm$

Hence, option b is correct i.e., 3√2 cm

Hope it helps...

Answer 2

Answer:

your answer is already done√√√√√√√√√√√√√√√√√√√