Question

solve it properly!!! ​

Answer 1

GIVEN :-

• Perimeter of an equilateral triangle is 36 cm

TO FIND :-

• Area and height of the equilateral triangle

SOLUTION :-

• Perimeter of a equilateral triangle is given by ,

• $\large{\underline {\boxed{ \bigstar{ | { \sf{ \: P = 3a}}}}}}$

Where ,

• a is side of the equilateral triangle

We have ,

• Perimeter of equilateral triangle as 36 cm

$\implies \sf \: 3a = 36 \\ \\ \implies \sf \: a = \frac{36}{3} \\ \\ \implies {\underline {\boxed {\pink{\sf {\: a = 12}}}}}$

Area of equilateral triangle is given by :-

$\large {\underline {\boxed {\bigstar {\sf{ \: A= \frac{ \sqrt{3} }{4} {a}^{2} }}}}}$

$\implies \sf \: A = \frac{ \sqrt{3} }{4} (12) {}^{2} \\ \\ \implies \sf \: A = \frac{ \sqrt{3} }{4} (144) \\ \\ \implies \sf \: A = \sqrt{3} (36) \\ \\ \implies {\underline{ \boxed {\blue {\sf{A = 36 \sqrt{3} \: cm {}^{2} }}}}}$

Height of an equilateral triangle is given by :-

$\large {\underline {\boxed {\bigstar {\sf{ \: H= \frac{ \sqrt{3}a }{2} }}}}}$

$\implies \sf \: H = \frac{ \sqrt{3} (12)}{2} \\ \\ \implies \sf \: H= \frac{ \sqrt{3}( \cancel{12}) }{ \cancel{2}} \\ \\ \implies \sf \: H = \sqrt{3} (6) \\ \\ \implies {\underline {\boxed {\blue{ \sf{H = 6 \sqrt{3} \: cm}}}}}$

∴ The height and area of the given equilateral triangle are $\large\sf{6\sqrt{3}}$ cm and $\large\sf{36\sqrt{3}}$ cm²

Answer 2

${\huge{\pink{\underbrace{\overbrace{\mathbb{\blue{ANSWER:-}}}}}}}$

The Perimeter of an equilateral triangle

= 3s         (s=side)

3s=36

s=12cm

Area of a equilateral triangle

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

=$\frac{\sqrt{4} }{3}\times 12\times 12$

=√3×4×12

=36√3 cm²

We know that area of a triangle is also,

$\frac{1}{2} \times b \times h$

So,

$\frac{1}{2}\times 12 \times h= 36$

6h=36

h=6cm

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