Question

the area of an equilateral. triangle is 36√3sq.cm.find it's perimeter pls answer fast
​

Answer 1

$\Large{\underline{\underline{\mathfrak{\red{\bf{Solution}}}}}}$

$\Large{\underline{\mathfrak{\orange{\bf{Given}}}}}$

• Area of equilateral triangle = 36√3 cm²

$\Large{\underline{\mathfrak{\orange{\bf{Find}}}}}$

• Perimeter of equilateral triangle

$\Large{\underline{\underline{\mathfrak{\red{\bf{Explanation}}}}}}$

Formula of Area of equilateral

$\boxed{\underline{\tt{\green{\:Area_{equilateral\:triangle}\:=\:(Side)^2\dfrac{\sqrt{3}}{4}}}}}$

$\boxed{\underline{\tt{\green{\:Perimeter_{equilateral\:triangle}\:=\:Sum\:of\:all\:side}}}}$

So, Now keep above values

➡ Area of equilateral triangle = (Side)² × √3/4

➡36√3 = (Side)² × √3/4

➡(Side)² = 36√3 × 4 / √3

➡(Side)² = 36 × 4

➡Side = √(6×6×2×2)

➡Side = 6 × 2

➡Side = 12 cm

$\Large{\underline{\mathfrak{\orange{\bf{Since}}}}}$

• Sides of equilateral triangle be = 12 cm

Now, Calculate perimeter of equilateral

➡Perimeter of equilateral triangle = 12 + 12 + 12

➡Perimeter of equilateral triangle = 36 cm

$\Large{\underline{\mathfrak{\orange{\bf{Hence}}}}}$

• Perimeter of equilateral triangle will be = 36 cm

_______________

Some Important Point

★ Equilateral triangle have same length of all sides.

_________________

Answer 2

$\Large{\underline{\underline{\mathfrak{\red{\bf{Solution}}}}}}$

$\Large{\underline{\mathfrak{\orange{\bf{Given}}}}}$

Area of equilateral triangle = 36√3 cm²

$\Large{\underline{\mathfrak{\orange{\bf{Find}}}}}$

Perimeter of equilateral triangle

$\Large{\underline{\underline{\mathfrak{\red{\bf{Explanation}}}}}}$

Formula of Area of equilateral

$\boxed{\underline{\tt{\green{\:Area_{equilateral\:triangle}\:=\:(Side)^2\dfrac{\sqrt{3}}{4}}}}}$

$\boxed{\underline{\tt{\green{\:Perimeter_{equilateral\:triangle}\:=\:Sum\:of\:all\:side}}}}$

So, Now keep above values

➡ Area of equilateral triangle = (Side)² × √3/4

➡36√3 = (Side)² × √3/4

➡(Side)² = 36√3 × 4 / √3

➡(Side)² = 36 × 4

➡Side = √(6×6×2×2)

➡Side = 6 × 2

➡Side = 12 cm

$\Large{\underline{\mathfrak{\orange{\bf{Since}}}}}$

Sides of equilateral triangle be = 12 cm

Now, Calculate perimeter of equilateral

➡Perimeter of equilateral triangle = 12 + 12 + 12

➡Perimeter of equilateral triangle = 36 cm

$\Large{\underline{\mathfrak{\orange{\bf{Hence}}}}}$

Perimeter of equilateral triangle will be = 36 cm

_______________

Some Important Point

★ Equilateral triangle have same length of all sides.

_________________