Question

If area of an equilateral traingle is√48 then find the value of its side

Answer 1

Step-by-step explanation:

$\blue{let \: the \: side \: of \: triangle = a \: cm} \\ \blue{ (\underline{note} : find \: height \: by \: pythagoreus \: theoram)}\\ \blue{height \: of \: triangle = \frac{ \sqrt{3} }{2} {a}^{2} } \\ \blue{area \: of \: triangle = \sqrt{48} \: {cm}^{2} } \\ \blue{\frac{1}{2} \times base \times height = \sqrt{48} } \\ \blue{ \frac{1}{2} \times a \times a\frac{ \sqrt{3} }{2} = \sqrt{48} } \\ \blue{ \frac{ \sqrt{3} }{4} {a}^{2} = \sqrt{48} } \\ \blue{ {a}^{2} = 4 \sqrt{ \frac{48}{3} } } \\ \blue{ {a}^{2} = 4 \sqrt{ 16} }\\ \blue{ {a}^{2} = 4 \times 4 = 16} \\ \blue{ a = \sqrt{ 16} } \\ \blue{a = 4 \: cm} \\ \\ \red{\mathfrak{\underline{\large{Hope \: It \: Helps \: You }}}} \\ \green{\mathfrak{\underline{\large{Mark \: Me \: Brainliest}}}}$