Find the side length of a triangle with an altitude of 30 yards?

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You left out the word "equilateral".

If you draw in the altitude, you form a pair of 30-60-90 right triangles. The ratios in this special triangle are:
(short leg) : (hypotenuse) : (long leg) = 1 : 2 : √3

In your case the long leg is the altitude and you want the hypotenuse which is a side.
(hypotenuse) : (long leg) = (side) : (altitude) = 2 / √3

The side is unknown (s) but the altitude is 30, so using proportions:
s/30 = 2/√3

Multiply both sides by 30:
s = 60/√3

But then rationalize the denominator by multiplying by √3/√3
s = (60 * √3) / (√3 * √3)
s = 60√3 / 3
s = 20√3...Show more