Question 985501


Height of an equilateral triangle is {{{5sqrt(3)}}} cm. Find its area & perimeter.
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In an equilateral triangle the height &nbsp;<B>h</B>&nbsp; is equal to 


{{{h}}} = {{{(a*sqrt(3))/2}}}, 


where &nbsp;{{{a}}}&nbsp; is the side measure. Hence, 


{{{a}}} = {{{(2h)/sqrt(3)}}}. 


In our case &nbsp;{{{a}}} = {{{(2*5sqrt(3))/sqrt(3)}}} = 10 cm. 


Therefore, the area of the triangle is 


{{{S}}} = {{{1/2}}}.{{{ah}}} = {{{1/2}}}.{{{10}}}.{{{5sqrt(3)}}} = {{{25sqrt(3)}}} {{{cm^2}}}. 


The perimeter is 


{{{P}}} = {{{3a}}} = 30 cm.