Question

If the area of an equilateral triangle is 36, find its perimeter. ​

Answer 1

Answer:

$\Large{\boxed{\underline{\overline{\mathfrak{\star \: QuEsTiOn :- \: \star}}}}}$

Find the perimeter of the equilateral triangle whose area is 36 units²

$\huge\underline{\overline{\mid{\bold{\pink{ANSWER-}}\mid}}}$

$\Large{\underline{\underline{\bf{GiVen:-}}}}$

❧ Area of an equilateral triangle is 36 units²

$\Large{\underline{\underline{\bf{To \: FiNd:-}}}}$

❧ Perimeter of the Equilateral Triangle

$\Large{\underline{\underline{\bf{SoLuTion:-}}}}$

Let the length of each side of the equilateral triangle be X units .

We know that,

$\star \: \boxed{ \sf \: Area_ {Equilateral \: Triangle} = { \dfrac{\sqrt{3}}{4} } \: {side}^{2} }$

$\longrightarrow \sf \: 36 = { \dfrac{\sqrt {3}}{4} } \: {side}^{2}$

$\longrightarrow \sf \: \sqrt{3} \: {side}^{2} = 36 \times 4$

$\longrightarrow \sf \: \sqrt{3} \: {side}^{2} = 144$

$\longrightarrow \sf \: \: {side}^{2} = \dfrac{144}{ \sqrt{3} }$

[√3 = 1.73]

$\longrightarrow \sf \: \: {side}^{2} = \cancel \dfrac{144}{ 1.73}$

$\longrightarrow \sf \: \: {side}^{2} = 83.23$

$\longrightarrow \sf \: \: side = \sqrt{83.23}$

$\longrightarrow \sf \: \: side =9.12 \: units \: \: \: (Approx)$

Now,

To calculate the perimeter of the triangle , multiply length of the side by 3

Let's find Perimeter of the Triangle

$\star \: \boxed{ \sf \: Perimeter_ {Equilateral \: Triangle} = 3 \times side}$

$\longrightarrow \sf \: 3 \times 9.12$

$\longrightarrow \sf \: 27.36 \: units \: \: \: (Approx)$

$\mathfrak{\huge{\purple{\underline{\underline{Hence}}}}}$

Perimeter of the Equilateral Triangle is 27.36 units.

Answer 2

• Refer to the attachment____