Question

The area of an equilateral triangle is 16√3m². Its perimeter is​

Answer 1

Given:

Area of equilateral ∆ = 16√3 m²

Let the side of equilateral ∆ = a m

Area of equilateral ∆ = (√3/4)a²

16√3 = (√3/4)a²

16√3 × (4/√3) = a²

64 = a²

a = √64

a =√ 8 × 8 = 8 m

Side of equilateral ∆ = 8 m

Perimeter of equilateral ∆ = 3 × side

Perimeter of equilateral ∆ = 3 × 8 = 24 m.

Hence, the perimeter of equilateral ∆ is 24 m.

HOPE THIS WILL HELP YOU....

Answer 2

$\;\;\underline{\textbf{\textsf{ Given:-}}}$

• Area of equilateral triangle = 16√3 m².

$\;\;\underline{\textbf{\textsf{ To Find :-}}}$

• Perimeter of the equilateral triangle

$\;\;\underline{\textbf{\textsf{ Solution :-}}}$

To find perimeter of equilateral triangle at first we need to find the side of equilateral triangle.

$\\ \underline{ \textsf{ We know that }}$

$\: \displaystyle \sf Area \: of \: equilateral \: triangle= \frac{ \sqrt{3} }{4} (side) ^{2}$

Given that,

• Area of equilateral triangle = 16√3 m²

$\\ \underline{ \bigstar \textsf{Putting the given values }}$

⇢$\: \displaystyle \sf \: 16 \sqrt{3} = \frac{ \sqrt{3} }{4} (side) ^{2}$

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

⇢$\: \displaystyle \sf \:64 \sqrt{3} = \sqrt{3} \times (side) ^{2}$

⇢$\: \displaystyle \sf \: \frac{64 \sqrt{3} }{ \sqrt{3} } = (side) ^{2}$

⇢$\: \displaystyle \sf \: (side) ^{2} = 64$

⇢$\: \displaystyle \sf \: side = \sqrt{64}$

$\bf{ ⇢ Side = 8\:m }$

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Again,

$\\ \underline{\textsf{ We know that }}$

$\displaystyle \sf \: Perimeter = 3 \times side$

$\\ \underline{ \bigstar \textsf{Putting the given values }}$

⇢$\displaystyle \sf \: Perimeter = 3 \times 8$

$\bf{ ⇢ Perimeter = 24\:m }$

$\;\;\underline{\textbf{\textsf{ Hence-}}}$

$\therefore \underline{ \textsf{Perimeter of equilateral triangle is 24 m.}}$

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