Question

The altitude of an equilateral triangle is 9 meters, what is the side length? (Hint: Draw a picture.)

Answer 1

The answer is 6sqrt3 because the sides of an equal triangle are in the ratio 2:1:sqrt3 This means that h = 9 = xsqrt3. Solving our equation we get:

9 = xsqrt3
9/(sqrt3) = x

Rationalizing the denominator gives us:

9sqrt3/(3) = x
3sqrt3 = x. 

Finally, because 2x equals the side of the triangle, we know that 6sqrt3 is the side length of the triangle.