Question

find yhe perimeter of equilateral triangle if it is area is 6 root 3 cm by solve​

Answer 1

Given :

• Area of equilateral triangle = 6√3 cm²

To find :

• perimeter of equilateral triangle

Formula used:

• A = √3/4 a²
• P = sum of all sides = a+a+a = 3a

where :-

• A = area of equilateral triangle
• a = length of side of equilateral triangle
• p = perimeter

Solution :

To find perimeter of equilateral triangle we must know the length of each side.

We will find length of each side by using the following formula :-

⟹ A = √3/4 a²

⟹ 6√3 = √3/4 a²

or

⟹ √3/4 a² = 6√3

⟹ √3/4 a² = 6√3

⟹ √3 a² = 6√3 × 4

⟹ a² = (6×4×√3)/ (√3)

⟹ a² = (6×4×√3)/ (√3)

√3 will cancel out from denominator and numerator

⟹ a² = 6×4

⟹ a² = 24

⟹ a = √24

⟹ a = √(2×2×2×3)

⟹ a = 2√(2×3)

⟹ a = 2√6 cm

Now we know length of each side. we will now find out perimeter :-

⟹ P = 3a

⟹ P = 3 × 2√6

⟹ P = 6√6 cm

Answer : 6√6 cm

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Learn more :-

Area of circle = πr²

Circumference of circle = 2πr

Area of square = (side)²

perimeter of square = 4× side

area of Rhombus = 1/2(diagonal 1)(diagonal 2)

Area of rectangle = length × breadth

Perimeter of rectangle = 2( length + breadth)

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