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

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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 $\frac{625}{12} \sqrt{3} ≅ 90.21$ $625/12 sqrt(3) ~=90.21$ to 2 decimal places

Explanation:

Consider the standardised equilateral triangle:
Tony B

The vertical height is $\sqrt{3}$ $sqrt(3)$ times $\frac{1}{2}$ $1/2$ the base

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

1 side = $\frac{25 \sqrt{3}}{3}$ $(25sqrt(3))/3$

Half of the base is $\frac{25 \sqrt{3}}{6}$ $color(brown)((25sqrt(3))/6)$

So the height is $\sqrt{3} \times \frac{25 \sqrt{3}}{6} = \frac{25}{2}$ $" " sqrt(3)xx(25sqrt(3))/6 =color(blue)( 25/2)$

Thus the area is $\frac{25}{2} \times \frac{25 \sqrt{3}}{6} = \frac{625}{12} \sqrt{3}$ $" "color(blue)(25/2)color(brown)(xx(25sqrt(3))/6)" "=" "color(green)(625/12 sqrt(3))$

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

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