How do you find the perimeter of an equilateral with an altitude of $6sqrt3$ cm?

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Answer 1 · 2015-11-30T21:38:02

Apply the Pythagorean theorem to solve for the side length and find that the perimeter is $36"cm"$

Drawing it out, we obtain the following picture:
enter image source here

Our goal is to find the perimeter, that is, $s+s+s=3s$

Looking at the right triangle with the sides marked in the picture, we can apply the Pythagorean theorem to get

$(s/2)^2 + h^2 = s^2$

$=> s^2/4 + h^2 = s^2$

$=> h^2 = 3/4s^2$

$=> s^2 = (4h^2)/3$

$=> s = sqrt((4h^2)/3)$

Substituting in our value for $h$ , we obtain

$s = sqrt((4*(6sqrt(3))^2)/3)$

$=sqrt((4*108)/3)$

$=sqrt(144)$

$=12$

Thus $3s = 3*12 = 36$

So the perimeter is $36"cm"$

How do you find the perimeter of an equilateral with an altitude of 6sqrt36sqrt3 cm?