Question

What is the length of each side of an equilateral triangle having an area of 4√3 cm²​

Answer 1

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

Need to find: The length of each side of equilateral triangle.

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀

⠀

$\underline{\bf{\dag} \:\mathfrak{As\: we \; know \; that \: :}}$⠀

⠀

$\star\:\boxed{\sf{\pink{Area \: of \: equilateral \: \triangle = \dfrac{\sqrt{3}}{\:4} (a)^2 \ cm}}}$

⠀⠀⠀⠀⠀⠀

• Here, a is each side of the equilateral triangle.

• Area of equilateral is 4√3 cm²

⠀

Therefore,

⠀

$:\implies\sf \dfrac{\cancel{\sqrt{3}}}{4} \: a^2 = 4\cancel{\sqrt{3}} \\\\\\:\implies\sf a^2 = 4 \times 4 \\\\\\:\implies\sf a^2 = 16 \\\\\\:\implies\sf a = \sqrt{16} \\\\\\:\implies{\underline{\boxed{\frak{\purple{a = 4\; cm}}}}}\;\bigstar$

⠀

$\therefore\:{\underline{\sf{Hence, \ Length \ of \:each\: side\; equilateral \ \triangle \ is \ \bf{4\;cm}.}}}$⠀⠀⠀

⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀⠀⠀

$\qquad\qquad\boxed{\bf{\mid{\overline{\underline{\pink{\bigstar\: More\;to\; know \: :}}}}}\mid}$

• Equilateral triangle is a triangle in which all the three sides have equal length.

• The sum of all three angles of an equilateral triangle is equal to 180°.

• Altitude of equilateral triangle = $\sf\dfrac{\sqrt{3}a}{2}$

• Perimeter of equilateral triangle = Sum of all sides. (a + a + a) = 3a

⠀

Answer 2

${\large{\bold{\rm{\underline{Understanding \; the \; question}}}}}$

This question says that we have to find out the length of each side of an equilateral triangle and it's area is given as 4√3 cm². Question is easy, it's already cleared that how to solve it properly and by using which formula. Let's solve it...!

${\large{\bold{\rm{\underline{Given \; that}}}}}$

${\sf{\bigstar Area \: of \: equilateral \: triangle \: = \: 4 \sqrt{3}}}$

${\large{\bold{\rm{\underline{To \; find}}}}}$

${\sf{\bigstar Length \: of \: each \: side \: of \: equilateral \: triangle}}$

${\large{\bold{\rm{\underline{Solution}}}}}$

${\sf{\bigstar Length \: of \: each \: side \: of \: equilateral \: triangle \: = \: 4 \: cm}}$

${\large{\bold{\rm{\underline{Using \; concept}}}}}$

${\sf{\bigstar Formula \: to \: find \: area \: of \: equaliteral \: triangle}}$

${\large{\bold{\rm{\underline{Using \; formula}}}}}$

${\sf{\bigstar Area \: of \: equaliteral \: triangle \: = \: \dfrac{\sqrt{3}}{4}(a)^{2}}}$

${\bf{Where,}}$

◕ a dented sides.

◕ √ means square root.

${\large{\bold{\rm{\underline{Full \; solution}}}}}$

${\bf{:\implies Area \: of \: equaliteral \: triangle \: = \: \dfrac{\sqrt{3}}{4}(a)^{2}}}$

${\bf{:\implies 4 \sqrt{3} \: = \dfrac{\sqrt{3}}{4}}}$

${\bf{:\implies 4 = \dfrac{1}{4}a^{2}}}$

${\bf{:\implies 4 \times 4 = a^{2}}}$

${\bf{:\implies 16 \: = a^{2}}}$

${\bf{:\implies \sqrt{16} \: = a}}$

${\bf{:\implies 4 = a}}$

${\bf{:\implies a = 4 \: cm}}$

${\green{\frak{Henceforth, \: 4 \: cm \: is \: the \: length \: of \: each \: side \: of \: equilateral \: triangle}}}$