Question

The are of equilateral triangle is numerically equal to its perimeter. Find its perimeter correct to 2decimal

Answer 1

And 4√3 = 6.92
 Perimeter = 6.92 *3
Perimeter = 20.76

Answer 2

Side of equilateral triangle = a units
Perimeter = 3a units
Area
$= \frac{ \sqrt{3} }{4} {a}^{2}$
Given that, Area = Perimeter
$\frac{ \sqrt{3} }{4} {a}^{2} = 3a$
$\sqrt{3} {a}^{2} = 3a \times 4$
$\sqrt{3} {a}^{2} = 12a$
$\sqrt{3} \times a \times a = 12 \times a$
$\sqrt{3} \times a = 12$
$a = \frac{12}{ \sqrt{3} }$
$a = \frac{4 \times 3}{ \sqrt{3} }$
$a = \frac{4 \times \sqrt{3} \times \sqrt{3} }{ \sqrt{3} }$
$a = 4 \sqrt{3}$
$a = 4 \times 1.73$
$( \sqrt{3} = 1.73)$
$a = 6.92 \: units$
Perimeter
$= 3a \\ = 3 \times 6.92 \\ = 20.76 \: units$