Question

an equilateral triangle are is 6√3cm^2 find it's perimeter​

Answer 1

Given:

• Area of equilateral triangle is 16√3 cm².

To Find:

• What is the perimeter of the triangle ?

Solution:

formula used,

${ \underline{ \boxed{ \bf{ \green{Area \: of \: Equilateral \: triangle= \frac{\sqrt{3}}{4}(a) ^{2} \: }}}}}$

According to Question

Putting values :

$:\implies \sf 16\sqrt{3 } =\frac{ \sqrt{3 }(a)^2}{4}$

$:\implies \sf \: 16\sqrt{3 } \times 4 = \sqrt{3 }(a)^2</p><p>$

$:\implies \sf 64\sqrt{3 } = \sqrt{3 }(a)^2$

$:\implies \sf\frac{ 64\sqrt{3 } }{\sqrt{3 }}= a^2</p><p>$

$:\implies \sf 64= a^2$

$:\implies \sf\sqrt{64} = a$

$:\implies \sf\sqrt{8} \times 8 = a$

$:\implies\bf\purple{a = 8 \: cm }$

Hence,

• The measure of each side of triangle is 8 cm.

$\\ { \underline{ \boxed{ \bf{ \red { Perimeter = 3 \times \: Side }}}}}$

$:\implies\sf{3 \times 8 \: }$

$:\implies\bf\pink{24 \: cm }$

Hence, the perimeter of equilateral triangle is 24 cm.