Question

. If the area of an equilateral triangle is16√ 3 cm

2 then the perimeter of the triangle is​

Answer 1

Answer:

area = (root3)/4*side^2

16 root3=root3 (r^2/4)

16=r^2/4

r^2=64

r=8

Answer 2

GivEn:

• Area of an Equilateral triangle is $\sf 16 \sqrt{3}\;cm$.

To find:

• Perimeter of triangle.

SoluTion:

Here, Area of an Equilateral triangle is $\sf 16 \sqrt{3}\;cm$.

⠀⠀⠀⠀

As we know that,

$\;\;\star\;{\boxed{\sf{\purple{Area\;of\; Equilateral\; \triangle = \dfrac{ \sqrt{3}}{4} \times (side)^2}}}}$

⠀⠀⠀⠀

Therefore,

$:\implies\sf \dfrac{ \sqrt{3}}{4} \times (side)^2 = 16 \sqrt{3}$

⠀⠀⠀⠀⠀⠀⠀

$:\implies\sf (side)^2 = 16 \cancel{ \sqrt{3}} \times \dfrac{4}{ \cancel{ \sqrt{3}}}$

⠀⠀⠀⠀

$:\implies\sf (side)^2 = 64$

⠀⠀⠀⠀

$:\implies\sf \sqrt{(side)^2} = \sqrt{64}$

⠀⠀⠀⠀

$:\implies{\underline{\boxed{\sf{\pink{side = 8\;cm}}}}}\;\bigstar$

⠀⠀⠀⠀

Therefore,

Perimeter of Equilateral triangle is,

⠀⠀⠀⠀

$:\implies\sf Perimeter = a + b + c$

⠀⠀⠀⠀

Where, a, b and c are equal.

⠀⠀⠀⠀

$:\implies\sf Perimeter = 8 + 8 + 8$

⠀⠀⠀⠀

$:\implies{\underline{\boxed{\sf{\purple{Perimeter = 24\;cm}}}}}\;\bigstar$

⠀⠀⠀⠀

$\therefore$ Hence, Perimeter of Equilateral triangle is 24 cm.