What is the perimeter of an equilateral triangle whose area is 25 sqrt3?

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Answer 1 · 2016-02-17T20:59:42

changed method of approach as not happy with first solution

Area is #625/12 sqrt(3) ~=90.21# to 2 decimal places

Consider the standardised equilateral triangle:
Tony B

The vertical height is #sqrt(3)# times #1/2# the base

Which is also the area. So we have for this question:

1 side =#(25sqrt(3))/3#

Half of the base is #color(brown)((25sqrt(3))/6\)#

So the height is#" " sqrt(3)xx(25sqrt(3))/6 =color(blue)( 25/2)#

Thus the area is #" "color(blue)(25/2)color(brown)(xx(25sqrt(3))/6)" "=" "color(green)(625/12 sqrt(3))#