Question

If the area of an equilateral triangle is9√3cm2 find the semi- parimeter of triangle

Answer 1

Answer:

9 cm

Step-by-step explanation:

Area of equilateral triangle = $\frac{\sqrt{3}}{4} *a^{2}$

$\ 9\sqrt{3}= \frac{\sqrt{3}}{4} *a^{2}\\9\sqrt{3}*4 = \sqrt{3} a^{2} \\36\sqrt{3} = \sqrt{3} a^{2}$

$\frac{\sqrt{3}*36}{\sqrt{3} } = a^{2} \\36 = a^{2}\\a = \sqrt{36} \\a = \sqrt{6*6}\\a = 6$

Now as we know perimeter is always sum of all the sides

So, Perimeter = a + a +a

= 6+6+6

= 18 cm

Half perimeter = 18/2 = 9 cm

Hope you get it