Question

The length of each side of an equilateral triangle of area 4√3 cm² is

4 cm

5 cm

√3/4 cm

3 cm

​

Answer 1

Step-by-step explanation:

Given : area of an equilateral triangle is 4√3 cm².

To find :  Length of each side of an equilateral triangle.

We will find the length of each side of an equilateral triangle by using the formula for area of an equilateral triangle :  

Area of an equilateral triangle ,A =  √3a²/4

A =  √3a²/4

4√3 = √3a²/4

4√3 × 4 = √3a²

16√3 = √3a²

a² = (16√3)/√3

a² = 16

a = √16

a = 4 cm

Hence, the length of each side of an equilateral triangle is 4 cm.

Option (A) 4 cm is correct.

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Answer 2

Answer:

Question :

The length of each side of an equilateral triangle of area 4√3 cm² is

• »» 4 cm
• »» 5 cm
• »» √3/4 cm
• »» 3 cm

$\rule{300}{1.5}$

Solution :

Here we have given that the area of equilateral triangle is 4√3 cm² and we need to find the each side of equilateral triangle. So, we'll use area of equilateral triangle formula :

${\longrightarrow{\small{\rm{Area_{(Equilateral Triangle)} = \dfrac{\sqrt{3}}{4} \times {(a)}^{2}}}}}$

Now, for finding the each side of equilateral triangle substituting all the given values in the formula :

$\begin{gathered} \quad{\longrightarrow{\rm{Area_{(Equilateral Triangle)} = \dfrac{\sqrt{3}}{4} \times {(a)}^{2}}}}\\\\\quad{\longrightarrow{\rm{Area_{(Equilateral Triangle)} = \dfrac{\sqrt{3}}{4} \times {(side)}^{2}}}}\\\\{\longrightarrow{\rm{4\sqrt{3} = \dfrac{\sqrt{3}}{4} \times {(side)}^{2}}}}\\\\{\longrightarrow{\rm{{(side)}^{2} = 4\sqrt{3} \times \frac{4}{\sqrt{3}}}}}\\\\ {\longrightarrow{\rm{{(side)}^{2} = 4 \cancel{\sqrt{3}} \times \frac{4}{\cancel{\sqrt{3}}}}}}\\\\ {\longrightarrow{\rm{{(side)}^{2} =4 \times 4}}}\\\\ {\longrightarrow{\rm{{(side)}^{2} =16}}}\\\\\quad{\longrightarrow{\rm{(side) = \sqrt{16}}}}\\\\ \quad{\longrightarrow{\rm{(side) = 4 \: cm}}} \\\\\quad\bigstar \: {\underline{\boxed{\sf{\red{side= 4 \: cm}}}}}\end{gathered}$

⌗ Hence, the lenght of each side of equilateral is 4 cm.

So, the option (1) 4 cm is the correct answer. ☑

$\rule{300}{1.5}$

Learn More :

$\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin{minipage}{9cm}\\ \dag\quad \Large\underline{\bf Formulas\:of\:Triangle:-}\\ \\ \star\sf Triangle \:area = \dfrac{1}{2}\times b \times h\\ \\ \star\sf Triangle \: perimeter=a+b+c\\\\ \star\sf Scalene\:\triangle=\sqrt{s (s-a)(s-b)(s-c)}\\\\\star\sf Equilateral\: \triangle\:area = \dfrac{\sqrt{3}}{4}\times{side}^{2}\\\\\star\sf Equilateral \:\triangle\:perimeter = 3 \times side\\\\\star\sf Isosceles\: \triangle\:area= \dfrac{3}{4}\sqrt{{4b}^{2}-{a}^{2}}\\\\\star\sf Isosceles\:\triangle\:perimeter=a+2b\end{minipage}}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered}$

$\underline{\rule{220pt}{3.5pt}}$