Question

find the height and area of an equilateral triangle whose perimeter is 12 metres
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Answer 1

Answer:

Height = root 12

Step-by-step explanation:

Area = 2 Root 12

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Answer 2

$\huge\mathbb{SOLUTION:-}$

$\sf\underline{\purple{\:\:\:\: Given\:\:\:\:}}$

The perimeter of equilateral∆ is 12 m

Now side = 12/3= 4

$\sf\bullet Side\:of\: equilateral\:triangle=4cm$

Now the Area of equilateral triangle

$\boxed{\sf{Area\:of\: equilateral\triangle=\dfrac{\sqrt{3}}{4}a{}^{2}}}$

$\boxed{\sf{Height\:of\: equilateral\:\triangle=\dfrac{\sqrt{3}}{2}a}}$

$\sf\underline{\purple{\:\:\:\: Solution\:\:\:\:}}$

Now the Area of ∆

$\sf\implies Area=\dfrac{\sqrt{3}}{4}\times (4){}^{2}\\ \\ \sf:\implies Area=\dfrac{\sqrt{3}}{\cancel4}\times \cancel{16}\\ \\ \sf:\implies Area=\sqrt{3}\times 4\\ \\ \sf:\implies Area=4\sqrt{3}cm{}^{2}$

Now the height of ∆

$\sf:\implies Height=\dfrac{\sqrt{3}}{\cancel2}\times \cancel{4}\\ \\ \sf:\implies Height=\sqrt{3}\times 2\\ \\ \sf:\implies Height=2\sqrt{3}cm$

$\boxed{\sf{Area\:of\: equilateral\triangle=4\sqrt{3}cm{}^{2}}}$

$\boxed{\sf{Height\:of\: equilateral\triangle=2\sqrt{3}cm}}$