Question

The area of an equilateral triangle is 4√3 cm2

. Its perimeter is

(a) 12 cm (b) 6 cm (c) 8 cm (d) 3√3 cm​

Answer 1

Answer:

Given :-

• The area of an equilateral triangle is 4√3 cm².

To Find :-

• What is the perimeter of an equilateral triangle.

Solution :-

Given :

• Area of an Equilateral Triangle = 4√3 cm²

According to the question by using the formula we get,

$\implies \sf\boxed{\bold{Area_{(Equilateral\: Triangle)} =\: \dfrac{\sqrt{3}}{4} a^2}}$

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

$\implies \sf \dfrac{4\cancel{\sqrt{3}} \times 4}{\cancel{\sqrt{3}}} =\: a^2$

$\implies \sf \dfrac{4 \times 4}{1} =\: a^2$

$\implies \sf \dfrac{16}{1} =\: a^2$

By doing cross multiplication we get,

$\implies \sf a^2 =\: 16(1)$

$\implies \sf a^2 =\: 16 \times 1$

$\implies \sf a^2 =\: 16$

$\implies \sf a =\: \sqrt{16}$

$\implies \sf a =\: \sqrt{\underline{4 \times 4}}$

$\implies \sf\bold{a =\: 4\: cm}$

Hence, the side of an equilateral triangle is 4 cm .

Now, we have to find the perimeter of an equilateral triangle :

Given :

• Side (a) = 4 cm

According to the question by using the formula we get,

$\implies \sf\boxed{\bold{Perimeter_{(Equilateral\: Triangle)} =\: 3a}}$

$\implies \sf Perimeter_{(Equilateral\: Triangle)} =\: 3 \times 4\: cm$

$\implies \sf\bold{\underline{Perimeter_{(Equilateral\: Triangle)} =\: 12\: cm}}$

$\therefore$ The perimeter of an equilateral triangle is 12 cm .

Hence, the correct options is option no (a) 12 cm .