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 $" "color(blue)(25/2)color(brown)(xx(25sqrt(3))/6)" "=" "color(green)(625/12 sqrt(3))$