Question

the perimeter of an equilateral triangle is 60m what will be its area?
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Answer 1

$\sf \bf \huge {\boxed {\mathbb {QUESTION}}}$

$\tt The\: perimeter\: of\: an \:equilateral\: triangle\: is \:60\:m \\\tt what\: will \:be\: its\: area?$

$\sf \bf \huge {\boxed {\mathbb {ANSWER}}}$

$\sf \bf {\boxed {\mathbb {GIVEN}}}$

• $\bf Perimeter \:of \:the \:equilateral \:triangle(P) = 60\:m$

$\sf \bf {\boxed {\mathbb {TO\:FIND}}}$

• $\bf Area\:of \:the \:equilateral \:triangle(A)$

$\sf \bf {\boxed {\mathbb {SOLUTION}}}$

${\pink {\underline {\bf {\pmb {Side\:of \:the \:equilateral \:triangle(a)}}}}}$

${\blue {\boxed {\boxed {\boxed {\green {\pmb {P=3a}}}}}}}$

• $\sf P=perimeter \:of \:the \:equilateral \:triangle$
• $\sf a=side \:of \:the \:equilateral \:triangle$

${\underbrace {\overbrace {\orange {\pmb {Substitute \:the \:values}}}}}$

$\bf \implies 60=3a$

$\bf \implies a=\dfrac{60}{3}$

$\bf \implies a=\dfrac{\cancel{60}}{\cancel{3}}$

$\implies {\blue {\boxed {\boxed {\purple {\sf a=20\:m}}}}}$

—————————————————————————————

${\pink {\underline {\bf {\pmb {Semiperimeter \:of \:the \:equilateral \:triangle(S)}}}}}$

${\blue {\boxed {\boxed {\boxed {\green {\pmb {S=\dfrac{P}{2}}}}}}}}$

• $\sf S=semiperimeter \:of \:the \:equilateral \:triangle$
• $\sf P=perimeter \:of \:the \:equilateral \:triangle$

${\underbrace {\overbrace {\orange {\pmb {Substitute \:the \:values}}}}}$

$\bf \implies S=\dfrac{60}{2}$

$\bf \implies S=\dfrac{\cancel{60}}{\cancel{2}}$

$\implies {\blue {\boxed {\boxed {\purple {\sf S=30\:m}}}}}$

—————————————————————————————

${\pink {\underline {\bf {\pmb {Area \:of \:the \:equilateral \:triangle(A)}}}}}$

${\orange{\sf {In \:equilateral \:triangle \:all\: sides \:are \:equal}}}$

$\longrightarrow {\boxed {\sf a=b=c=20}}$

${\blue {\boxed {\boxed {\boxed {\green {\pmb {A=\sqrt{S\Big(S-a\Big)\Big(S-b\Big)\Big(S-c\Big)}}}}}}}}$

• $\sf S=semiperimeter \:of \:the \:equilateral \:triangle$
• $\sf A=area\:of \:the \:equilateral \:triangle$
• $\sf a=side \:of \:the \:equilateral \:triangle$

${\underbrace {\overbrace {\orange {\pmb {Substitute \:the \:values}}}}}$

$\bf \implies A=\sqrt{30\Big(30-20\Big)\Big(30-20\Big)\Big(30-20\Big)}$

$\bf \implies A=\sqrt{30\Big(10\Big)\Big(10\Big)\Big(10\Big)}$

$\bf \implies A=\sqrt{30\times 10\times 10\times 10}$

$\bf \implies A=\sqrt{30000}$

$\bf \implies A=\sqrt{10000\times 3}$

$\implies {\blue {\boxed {\boxed {\purple {\mathfrak {A=100\sqrt{3}\:{m}^{2}}}}}}}$

${\underbrace {\red {\overline {\red {\underline {\red {\sf {\pmb {{\therefore} The\:area \:of \:the \:equilateral \:triangle \:is\:100\sqrt{3}\:{m}^{2}}}}}}}}}}$

$\sf \bf \huge {\boxed {\mathbb {HOPE \:IT \:HELPS \:YOU}}}$

___________________________________________

$\sf \bf \huge {\boxed {\mathbb {EXTRA\:INFORMATION}}}$

$\sf Area\:of \:triangle = \dfrac{1}{2}bh$

$\sf Perimeter \:of \:triangle =a+b+c$

Answer 2

Answer:

Correct option is

B

100

3

m

2

Perimeter of equilateral triangle =3×side

60=3×sides

Side=20 cm

Area of equilateral triangle =

4

3

×(side)

2

=

4

3

×20×20

=100

3

cm

2