Question

the longest of each side of an equilateral triangle of area 4 root 3 cm square​

Answer 1

AnsWer :

4 Cm.

Given :

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

• Area of equilateral triangle is 4√3 cm².
• And, it sides.

Required Formula :

• Area of equilateral triangle = √3 /4 a².
• Here, a show sides of equilateral triangle.

Solution :

Let Sides of equilateral triangle be ABC,

Now, Putting the above given value.

Area of equilateral triangle =

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

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

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

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

$\tt\dashrightarrow a = 4 \: cm.$

Therefore, the sides of equilateral triangle be 4 cm.

$\rule{200}1$

Some information :

All about the equilateral triangle,

• It have all sides equal.
• Each angle 60.
• Area of equilateral triangle is √3/4a².

Answer 2

Given :-

Area of equilateral triangle = 4√3 sq.cm

$\huge{ \underline{ \underline{ \blue{ \sf{SoLuTiOn :-}}}}}$

Let the side of equilateral triangle = a cm

We know that

${\purple{\boxed{\large{\bold{</u><u>A</u><u>rea \: of \: equilateral \: \triangle \: = \frac{ \sqrt{3} }{4} {a}^{2} }}}}}$

where a is side of triangle .

$\implies4 \sqrt{3} = \frac{ \sqrt{3} }{4} {a}^{2} \\ \\ \implies4 \times 4 \sqrt{3} = \sqrt{3} {a}^{2} \\ \\ \implies16 \sqrt{3} = \sqrt{3} {a}^{2} \\ \\ \implies \: \frac{16 \sqrt{3} }{ \sqrt{3} } = {a}^{2} \\ \\ \implies {a}^{2} = 16 \\ \\ \implies \: a = \sqrt{16} \\ \\ \implies \: a = \sqrt{4 \times 4} \\ \\ \implies \: a = 4$

Therefore ,

${\red{\boxed{\large{\bold{The \:side \:of \: equilateral \:triangle = 4 cm}}}}}$