Question

Find the length of each side of an equilateral triangle having an area of 9√3 〖cm〗^2

Answer 1

Answer:

6 cm

Step-by-step explanation:

area of eq triangle = root3/4 *asquare  where a is a side of triangle put the value and get answer

Answer 2

AnsWer :

6 Cm.

Solution :

$\setlength{\unitlength}{0.78 cm}\begin{picture}(12,4)\thicklines\put(5.4,5.8){ A }\put(11.2,5.8){ B }\put(8.4,10){ C }\put(6,6){\line(2,3){2.5}}\put(11,6){\line(-2,3){2.5}}\put(6,6){\line(1,0){5}}\put(5,7.9){ 6\:cm }\put(11,7.9){ 6\:cm }\put(8,5){ 6\:cm }\end{picture}$

Area of equilateral triangle = 9√3.

$\tt\dashrightarrow \frac{ \sqrt{3} }{4} {a}^{2} .$

Putting the above given value,

$\tt\dashrightarrow \frac{ \sqrt{3} }{4} {a}^{2} = 9 \sqrt{3} .$

$\tt\dashrightarrow {a}^{2} = 9 \times 4.$

$\tt\dashrightarrow a = \sqrt{9 \times 4} .$

$\tt\dashrightarrow a = \sqrt{36}.$

$\tt\dashrightarrow a = \pm6.$

Here, Length never be negative,

$\tt\dashrightarrow \red{a \neq - 6.}$

Therefore, each sides of equilateral triangle be 6 Cm.