Question

The area of an equilateral triangle is numeri-
cally equal to its perimeter. Find its perimeter
correct to 2 decimal places.​

Answer 1

Answer:

$Perimeter ≈20.78$

Step-by-step explanation:

$Let \: side \: of \: an \\equilateral \: triangle = a$

According to the problem given,

$Area \: of \: the \: triangle\\ = Perimeter$

$\implies \frac{\sqrt{3}}{4} \times a^{2}=3a$

$\implies \frac{\sqrt{3}}{4} \times a=3$

$\implies a = \frac{3\times 4}{\sqrt{3}}$

$\implies a = 4\sqrt{3}\\=4\times 1.732\\=6.928$

Therefore,

$Perimeter = 3a \\=3\times 6.928\\=20.784\\≈20.78$

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