Question

Z. If the area of an equilateral triangle is 36/3 cm ?, find its perimeter.​

Answer 1

Step-by-step explanation:

Area of an Equilateral triangle = \frac{ \sqrt{3} }{4}

4

3

a²

a = side of each side of the triangle

Now equating,

\frac{ \sqrt{3} }{4}

4

3

a² = 36√3

a² = \frac{36 \sqrt{3}* 4}{ \sqrt{3} }

3

36

3

∗4

[√3 gets cancelled]

a² = 36×4

a = √6×6×2×2 = 12cm

Hence, side= 12cm

Perimeter = (Side + Side + Side)

= (12 + 12 + 12) cm = 36 cm .

Answer 2

Correct question :-

If the area of an equilateral triangle is 36√3 cm, find its perimeter.​

Given :-

Area of an equilateral triangle = 36√3 cm

To Find :-

The perimeter of an equilateral triangle.

Solution :-

We know that,

• a = Area
• p = Perimeter

By the formula,

$\underline{\boxed{\sf Area \ of \ a \ equilateral \ triangle=\dfrac{\sqrt{3} }{4} a^2}}$

Given that,

Area (a)= 36√3 cm

Substituting their values,

√3/4 a² = 36√3

a² = 36√3×4/√3

a² = 36 × 4

a = √6×6×2×2

a = 12 cm

Therefore, the side of an equilateral triangle is 12 cm.

By the formula,

$\underline{\boxed{\sf Perimeter \ of \ a \ equilateral \ triangle=Side + Side + Side}}$

Given that,

Side (s) = 12 cm

Substituting their values,

p = (12 + 12 + 12)

p = 36 cm

Therefore, the perimeter of the triangle is 36 cm.