Question

if the area of an equilateral triangle is 36√3cm find its perimeter (cm)​

Answer 1

Question :-

if the area of an equilateral triangle is 36√3cm find its perimeter (cm).

Answer :-

• Perimeter = 36cm.

Step by step explanation :-

Here, we have the area of equilateral triangle is $36 \sqrt{3}$ cm. We have to find it's perimeter, because of that first we have to find the side of equilateral triangle. If we have side then we easily find the perimeter of equilateral triangle.

Finding Side of equilateral triangle,

Using formula,

$\rm:\longmapsto\red{Area_{(Equilateral \: triangle)} = \frac{ \sqrt{3} }{4} a {}^{2} }$

• Note - a means side

Substituting the value of area of equilateral triangle,

$\rm:\longmapsto{36 \sqrt{3} = \frac{ \sqrt{3} }{4}a {}^{2} } \: \: \: \: \\ \\\rm:\longmapsto{a {}^{2} = \frac{36 \: \cancel{ \sqrt{3} } \times 4}{ \cancel{ \sqrt{3}} } } \: \\ \\ \rm:\longmapsto{a {}^{2} = 36 \times 4} \: \: \: \: \: \: \: \: \\ \\ \rm:\longmapsto{a {}^{2} = 144 } \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \rm:\longmapsto{a = \sqrt{144} } \: \: \: \: \: \: \: \: \: \: \: \\ \\ \rm:\longmapsto \red{a = 12cm} \: \: \: \: \: \: \: \: \: \: \:$

Finding Perimeter of equilateral triangle,

Using formula,

$\rm:\longmapsto \red{Perimeter_{(Equilateral \: triangle) }= 3a}$

$\rm:\longmapsto{3a} \: \: \: \: \: \: \\ \\ \rm:\longmapsto{3(12)} \: \\ \\ \rm:\longmapsto \red{36cm}$

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