Question

if the perimeter of an equilateral triangle is 450 cm find its area and altitude use root 3=1.73

Answer 1

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Answer 2

$area \: of \: eq. \: triangle \: using \: herons \: formula \: is \: given \: by \\ \\ \ \frac{ \sqrt{3}a }{4} \: where \: a \: is \: the \: side \\ \\ plugging \: in \: values \\ \ \frac{ \sqrt{3} \times 150 }{4} \: \: \: (as \: side \: = \frac{perimeter}{3} ) \\ \\ = \: \frac{1.73 \times 150}{4} = \frac{259.5}{4} \\ \\ = 64.875 \: {cm}^{2} \\ \\ but \: ar(triangle) \: is \: also \: given \: by \: \frac{1}{2} b \times h \\ \\ therefore \: 64.875 = \frac{1}{2} \times 150 \times h \\ \\h = \frac{129.175}{150} = 0.865 \: cm$