Question

The perimeter of an equilateral triangle is 60 M find its area or construct an angle of 30°.​

Answer 1

$\huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

• Perimeter = 60 m
• Sides of Equilateral Triangle are equal

So,

★$\large {\boxed{\sf{Perimeter \: = \: Sum \: of \: Sides}}}$

$\implies {\sf{60 \: = \: Side \: + \: Side \: + \: Side}}$

$\implies {\sf{60 \: = \: 3 \: \times \: Side}}$

$\implies {\sf{Side \: = \: \dfrac{\cancel{60}}{\cancel{3}}}}$

$\implies {\sf{Side \: = \: 20 \: m}}$

$\rm{\therefore \: Side \: is \: of \: 20 \: m}$

$\rule{200}{1}$

And formula for Area is

★$\large {\boxed{\sf{Area \: = \: \dfrac{\sqrt{3}}{4} \: Side^2}}}$

$\implies {\sf{Area \: = \: \dfrac{\sqrt{3}}{4} \: (20)^2}}$

$\implies {\sf{Area \: = \: \dfrac{\sqrt{3}}{\cancel{4}} \: \cancel{400}}}$

$\implies {\sf{Area \: = \: 100 \sqrt{3}}}$

$\leadsto {\boxed{\sf{Area \: = \: 100 \sqrt{3} \: m^2}}}$

Answer 2

◦•●◉✿ SOLUTION✿◉●•◦

✿ GIVEN✿

•The perimeter of an equilateral ∆=60m

☀ FIND:-The area of Triangle

⟶(✱° PERIMETER=Sum of all sides °✱)

$⟶perimeter = 3 \times side \\ ⟶60 = 3 \times side \\ ⟶side = 20m$

Hence:-

☀ The Area of equilateral triangle

$⟶ \frac{ \sqrt{3} }{4} \times {20}^{2} \\ \\ ⟶ \frac{ \sqrt{3} }{4} \times 20 \times 20 \\ \\ ⟶100 \sqrt{3} {m}^{2}$