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  • If the area of an equilateral triangle is 16 sqrt{3}cm^{2}, then the perimeter of the triangle is: (A) 48 cm (B) 24 cm (C) 12 cm (D) 36 cm

If the area of an equilateral triangle is 16\sqrt{3}cm^{2}, then the perimeter of the triangle is:

(A) 48 cm

(B) 24 cm

(C) 12 cm

(D) 36 cm

Answers (1)

[B]

Given the area of the equilateral triangle = 16\sqrt{3}cm^{2}

Suppose the side of the equilateral triangle is = a cm

We know that,

Area of equilateral triangle = \frac{\sqrt{3}}{4}\left ( side \right )^{2}

16\sqrt{3}\; = \frac{\sqrt{3}}{4}\times \left ( a \right )^{2}

16\times 4\times \sqrt{3}= \sqrt{3}\times \left ( a \right )^{2}

\frac{64\times \sqrt{3}}{\sqrt{3}}= a^{2}

a2 = 64

a = \sqrt{64}

a = 8 cm

Perimeter = 3a = 3(8) = 24 cm

Hence option (B) is correct.

 

Posted by

infoexpert21

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