Question

the area of an equilateral triangle is 16v3 cm, then its perimeter is
(b) 24 cm
(c) 12 cm
(d) 36 cm
al 48 cm​

Answer 1

GIVEN:

• Area of an equilateral triangle is 16√3 cm²

TO FIND:

• What is the perimeter of the triangle ?

SOLUTION:

Let the side of an equilateral triangle be 'x' cm

We know that the formula for finding the area of an equilateral triangle is:-

$\large{\boxed{\bf{\star \: AREA = \dfrac{\sqrt{3}}{4} \times (side)^2\: \star}}}$

Let the side of an equilateral triangle be 'a' cm

According to question:-

On putting the given values in the formula, we get

$\rm{\dashrightarrow 16\sqrt{3} = \dfrac{\sqrt{3}}{4} \times (a)^2 }$

$\rm{\dashrightarrow 16\sqrt{3} \times 4 = \sqrt{3} \times a^2 }$

$\rm{\dashrightarrow 64 \sqrt{\cancel{3}} = \sqrt{\cancel{3}} \times a^2 }$

$\rm{\dashrightarrow 64 = a^2 }$

$\rm{\dashrightarrow \sqrt{64} = a }$

$\large\bf{\dashrightarrow 8 \: cm = a }$

We know that the formula for finding the perimeter of the triangle is:-

$\large{\boxed{\bf{\star \: Perimeter = 3 \times side \: \star}}}$

According to question:-

$\rm{\dashrightarrow Perimeter = 3 \times 8 }$

$\large\bf{\dashrightarrow Perimeter = 24 \: cm }$

❝ Hence, the perimeter of an equilateral triangle is 24 cm ❞

______________________

Answer 2

Given :-

• The are of an equilateral triangle is 16√3 cm².

To find :-

• The perimeter of equilateral triangle = ?

Solution :-

$\dagger\:$ $\boxed{\pink{\sf Area = \dfrac{\sqrt{3}}{4} \times \left(side \right)^{2}}}$

$\dashrightarrow\:$ $\sf 16\sqrt{3} = \dfrac{\sqrt{3}}{4} \times \left(a \right)^{2}$

$\dashrightarrow\:$ $\sf 16 \sqrt{3} \times 4 = \sqrt{3} \times (a)^{2}$

$\dashrightarrow\:$ $\sf 64 = (a)^{2}$

$\dashrightarrow\:$ $\red{\sf a = 8 \:cm}$

Hence, area of equilateral triangle is 8 cm.

$\dagger\:$ $\boxed{\pink{\sf Perimeter = 3 \times \left(side \right)}}$

$\dashrightarrow\:$ $\sf 3 \times 8$

$\dashrightarrow\:$ $\underline{\boxed{\green{ \textbf{Perimeter = 24 \:cm}}}}$ $\red\bigstar$

Therefore, the perimeter of equilateral triangle is 24 cm.