Question

Area of an equilateral triangle is given by
A = √3 a², where A= area, a= side, find the
perimeter if A=1653 cm²
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Answer 1

Given:

• Area of an equilateral Δgle = (√3/4) × a²

• Area of the triangle (A) = 1653 cm²

• A = area; a = side

To Find:

• Perimeter = ?

Solution:

We'll equate the area of the triangle with the formula used to find the area of the triangle, find the value of the sides, then multiply it by 3 to find the perimeter.

$\sf \Longrightarrow \dfrac{\sqrt{3} \ }{4} \ a^2 = 1653 \ cm^2}$

$\sf \Longrightarrow \sqrt{3}a^2 = 1653 \times 4\ cm^2$

$\sf \Longrightarrow \sqrt{3}a^2 = 6612 cm^2$

$\sf \Longrightarrow a^2 = \dfrac{6612}{\sqrt{3} \ }$

Rationalizing the denominator;

$\sf \Longrightarrow a^2 = \dfrac{6612}{\sqrt{3} \ } \times \dfrac{\sqrt{3}}{\sqrt{3}}$

$\sf \Longrightarrow a^2 = \dfrac{6612\sqrt{3}}{3}$

$\sf \Longrightarrow a^2 = 2204\sqrt{3}$

$\sf \Longrightarrow a^2 = 2204 \times 1.732$

$\sf \Longrightarrow a^2 = 3817.32$

$\sf \Longrightarrow a = \sqrt{3817.32}$

$\sf \Longrightarrow a \simeq 61.78452$

$\sf \Longrightarrow a \simeq 61.79$

⇒ Perimeter of the Δgle ≈ 3 × side

⇒ Perimeter of the Δgle ≈ 3 × 61.79

⇒ Perimeter of the Δgle ≈ 185.37

(Answer might vary depending on what value you take for √3)